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CBSE Class 10 Maths Case Study Questions for Chapter 2 - Polynomials (Published by CBSE)

Check the case study questions published by cbse for class 10 maths chapter 2 - polynomials. these questions are important for the preparation of cbse class 10 maths exam 2021-22..

CBSE Class 10 Maths paper in Board Exam 2022 will have some questions based on the case study. These questions are entirely new for the class 10 students. Therefore, the board has released a question bank to help the students get familiarised with the case study questions. We have provided here the case study questions for CBSE Class 10 Maths Chapter 2 - Polynomials. All the questions have sub-questions of MCQ type. You can find the answer (correct option) written against each question. Practice all the case study based questions right after you finish with the chapter - Polynomials. This will help you prepare for your Maths exam easily and effectively.

Case Study Questions for Class 10 Maths Chapter 2 - Polynomials

CASE STUDY 1:

The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

1. In the standard form of quadratic polynomial, ax 2 + bx + c, a, b and c are

a) All are Polynomials.

b) All are rational numbers.

c) ‘a’ is a non zero real number and b and c are any Polynomials.

d) All are integers.

Answers: c) ‘a’ is a non zero real number and b and c are any Polynomials.

2. If the roots of the quadratic polynomial are equal, where the discriminant D = b 2 – 4ac, then

a) D > 0

b) D < 0

c) D ≥ 0

Answers: d) D = 0

3. If α and 1/α are the zeroes of the quadratic polynomial 2x2 – x + 8k, then k is

c) –1/4

Answers: b) 1/4

4. The graph of x 2 +1 = 0

a) Intersects x‐axis at two distinct points.

b)Touches x‐axis at a point.

c) Neither touches nor intersects x‐axis.

d)Either touches or intersects x‐ axis.

Answers: c) Neither touches nor intersects x‐axis.

5. If the sum of the roots is –p and product of the roots is –1/p, then the quadratic polynomial is

a) k(–px 2 + x/p + 1)

b) k(px 2 – x/p – 1)

c) k(x 2 + px – 1/p)

d) k(x 2 – px + 1/p)

Answers: c) k(x 2 + px – 1/p)

CASE STUDY 2:

An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

1. The shape of the poses shown is

d) Parabola

Answer: d) Parabola

2. The graph of parabola opens downwards, if _______

a) a ≥ 0

c) a < 0

d) a > 0

Answer: c) a < 0

3. In the graph, how many zeroes are there for the polynomial?

Answer: c) 2

4. The two zeroes in the above shown graph are

Answer: b) -2, 4

CASE STUDY 3:

Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.

1. The shape of the path traced shown is

2. The graph of parabola opens upwards, if _______

b) a < 0

c) a > 0

d) a ≥ 0

Answer: c) a > 0

3. Observe the following graph and answer

In the above graph, how many zeroes are there for the polynomial?

Answer: d) 3

4. The three zeroes in the above shown graph are

b) -2, 3, 1

c) -3, -1, 2

d) -2, -3, -1

Answer: c) -3, -1, 2

5. What will be the expression of the polynomial?

a) x 3 + 2x 2 – 5x – 6

b) x 3 + 2x 2 – 5x + 6

c) x 3 + 2x 2 + 5x – 6

d) x 3 + 2x 2 + 5x + 6

Answer: a) x 3 + 2x 2 – 5x – 6

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

Tips to Solve Case Study Based Questions Accurately

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CBSE 10th Standard Maths Subject Polynomials Case Study Questions With Solution 2021

By QB365 on 21 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) The expression of the polynomial represented by the graph is

-49

-64

-36

-81

(iii) Find the value of the polynomial represented by the graph when x = 6.

(iv) The sum of zeroes of the polynomial x 2  + 2x - 3 is

(v) If the sum of zeroes of polynomial at 2  + 5t + 3a is equal to their product, then find the value of a.

(ii) Find the value of \(\alpha\) + \(\beta\) +  \(\alpha\) \(\beta\) .

(iii) The value of p(2) is

(iv) If \(\alpha\) and \(\beta\) are zeroes of  \(x^{2}+x-2, \text { then } \frac{1}{\alpha}+\frac{1}{\beta}=\)

(v) If sum of zeroes of  \(q(x)=k x^{2}+2 x+3 k\)  is equal to their product, then k =

(ii) The axis of symmetry of the given parabola is

(iii) The zeroes of the polynomial, represented in the given graph, are

(iv) Which of the following polynomial has -2 and -3 as its zeroes?

\((a) x^{2}-5 x-5\)

\((b) x^{2}+5 x-6\)

\((c) x^{2}+6 x-5\)

\((d) x^{2}+5 x+6\)

(v) For what value of 'x', the value of the polynomial  \(f(x)=(x-3)^{2}+9 \text { is } 9 ?\)

(ii) What will be the expression of the polynomial given in diagram?

\((a) x^{2}-6 x+16\)

\((b) -x^{2}+6 x+16\)

\((c) x^{2}+6 x+16\)

\((d) -x^{2}-6 x-16\)

(iii) What is the value of the polynomial, represented by the graph, when x = 4?

(iv) If the tunnel is represented by x 2  + 3x - 2, then its zeroes are

(v) If one zero is 4 and sum of zeroes is -3, then representation of tunnel as a polynomial is

\((a) x^{2}-x+24\)

\((b) -x^{2}-3 x+28\)

\((c) x^{2}+x+28\)

\((d) x^{2}-x+28\)

(ii) The sum of product of zeroes taken two at a time is

(iii) Product of zeroes of polynomial p(x) is

(iv) The value of the polynomial p(x), when x = 4 is

(v) If  \(\alpha,\beta,\gamma\)  are the zeroes of a polynomial g(x) such that  \(\alpha+\beta+\gamma=3, \alpha \beta+\beta \gamma+\gamma \alpha=-16\)   and  \(\alpha \beta \gamma=-48\)   then, g(x) =

*****************************************

Cbse 10th standard maths subject polynomials case study questions with solution 2021 answer keys.

(i) (b): Graph of a quadratic polynomial is a parabolic in shape. (ii) (c): Since the graph of the polynomial cuts the x-axis at (-6,0) and (6, 0). So, the zeroes of polynomial are -6 and 6. \(\therefore\) Required polynomial is p(x) = x 2 - (-6 + 6)x + (-6)(6) = x 2 - 36 (iii) (c) : We have, p(x) = x 2 - 36 Now, p( 6) = 62 - 36 = 36 - 36 = 0 (iv) (b): Letf (x) = x 2 + 2x - 3. Then, \(\text { Sum of zeroes }=-\frac{\text { coefficient of } x}{\text { coefficient of } x^{2}}=-\frac{(2)}{1}=-2\) (v) (d): The given polynomial is at 2 + 5t + 3a Given, sum of zeroes = product of zeroes. \(\Rightarrow \quad \frac{-5}{a}=\frac{3 a}{a} \Rightarrow a=\frac{-5}{3}\)

(i) (b): Given, a and \(\beta\) are the zeroes of  \(p(x)=x^{2}-24 x+128\) \(\text { Putting } p(x)=0 \text { , we get }\) \( x^{2}-8 x-16 x+128=0 \) \(\Rightarrow x(x-8)-16(x-8)=0 \) \(\Rightarrow (x-8)(x-16)=0 \Rightarrow x=8 \text { or } x=16 \) \(\therefore \alpha=8, \beta=16\) (ii) (c) :  \(\alpha+\beta+\alpha \beta =8+16+(8)(16) =24+128=152 \) (iii) (d) :  \(p(2)=2^{2}-2 4(2)+128=4-48+128=84\) (iv) (a): Since a and \(\beta\) are zeroes of  \(x^{2}+x-2\) \(\therefore \quad \alpha+\beta=-1 \text { and } \alpha \beta=-2 \) \(\text { Now, } \frac{1}{\alpha}+\frac{1}{\beta}=\frac{\beta+\alpha}{\alpha \beta}=\frac{-1}{-2}=\frac{1}{2}\) (v) (c): Sum of zeroes  \(=\frac{-2}{k}\) Product of zeroes  \(=\frac{3 k}{k}=3\) According to question, we have  \(\frac{-2}{k}=3\) \(\Rightarrow \quad k=\frac{-2}{3}\)

(i) (b): The shape of the path of the soccer ball is a parabola. (ii) (c): The axis of symmetry of the given curve is a line parallel to y-axis. (iii) (a): The zeroes of the polynomial, represented in the given graph, are -2 and 7, since the curve cuts the x-axis at these points. (iv) (d): A polynomial having zeroes -2 and -3 is  \(p(x)=x^{2}-(-2-3) x+(-2)(-3)=x^{2}+5 x+6\) (v) (c): We have  \(f(x)=(x-3)^{2}+9\) \(\text { Now, } 9=(x-3)^{2}+9 \) \(\Rightarrow(x-3)^{2}=0 \Rightarrow x-3=0 \Rightarrow x=3\)

(i) (a): Since, the graph intersects the x-axis at two points, namely x = 8, -2. So, 8, - 2 are the zeroes of the given polynomial. (ii) (b): The expression of the polynomial given in diagram is  \(-x^{2}+6 x+16\) (iii) (c) : Let  \(p(x)=-x^{2}+6 x+16\) \(\text { When } x=4, p(4)=-4^{2}+6 \times 4+16=24\) (iv) (d): Let  \(f(x)=-x^{2}+3 x-2\) Now, consider  \(f(x)=0 \Rightarrow-x^{2}+3 x-2=0\) \(\begin{aligned} &\Rightarrow x^{2}-3 x+2=0 \Rightarrow(x-2)(x-1)=0\\ &\Rightarrow x=1,2 \text { are its zeroes. } \end{aligned}\) (v) (b): Let a and \(\beta\)  are the zeroes of the required polynomial. Given  \(\alpha + \beta = - 3\) If \(\alpha\) = 4, then  \(\beta\) = -7 \(\therefore \quad \text { Representation of tunnel is }-x^{2}-3 x+28 \text { . }\)

(i) (c): For finding  \(\alpha,\beta,\)   \(\gamma\)  consider p(x) = 0 \(\Rightarrow \quad x^{3}-18 x^{2}+95 x-150=0 \) \(\Rightarrow \quad(x-3)\left(x^{2}-15 x+50\right)=0 \) \(\Rightarrow \quad(x-3)(x-5)(x-10)=0 \Rightarrow x=10 \text { or } x=5 \text { or } x=3 \) \(\text { Thus } \alpha=10, \beta=5 \text { and } \gamma=3\) (ii) (d): Here  \(\alpha=10, \beta=5 \text { and } \gamma=3\) \(\therefore\)   Sum of product of zeroes taken two at a time \(\begin{array}{l} =\alpha \beta+\beta \gamma+\gamma \alpha=(10)(5)+(5)(3)+(3)(10) \\ =50+15+30=95 \end{array}\) (iii) (a): Product of zeroes of polynomial p(x) =  \(\alpha\beta\gamma\) = (10) (5) (3) = 150 (iv) (b): We have  \(p(x)=x^{3}-18 x^{2}+95 x-150\) \(\begin{array}{l} \text { Now, } p(4)=4^{3}-18(4)^{2}+95(4)-150 \\ =64-288+380-150=6 \end{array}\) (v) (d):   \(g(x)=x^{3}-(\alpha+\beta+\gamma) x^{2} +(\alpha \beta+\beta \gamma+\gamma \alpha) x-\alpha \beta \gamma \) \(\Rightarrow g(x)=x^{3}-3 x^{2}-16 x-(-48)=x^{3}-3 x^{2}-16 x+48\)

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Class 10 Maths Case Study Questions Chapter 2 Polynomials

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Case study Questions in the Class 10 Mathematics Chapter 2  are very important to solve for your exam. Class 10 Maths Chapter 2 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 2  Polynomials

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In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Polynomials Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 2 Polynomials

Case Study/Passage-Based Questions

Question 1:

Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoors on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of a parabola representing quadratic polynomial.

1. The shape of the path traced shown is

d) Parabola

Answer: d) Parabola

2. The graph of parabola opens upwards, if _______

b) a < 0

c) a > 0

Answer: c) a > 0

3. Observe the following graph and answer

In the above graph, how many zeroes are there for the polynomial?

Answer: d) 3

4. The three zeroes in the above shown graph are

b) -2, 3, 1

c) -3, -1, 2

d) -2, -3, -1

Answer: c) -3, -1, 2

5. What will be the expression of the polynomial?

a) x 3  + 2x 2  – 5x – 6

b) x 3  + 2x 2  – 5x + 6

c) x 3  + 2x 2  + 5x – 6

d) x 3  + 2x 2  + 5x + 6

Answer: a) x3 + 2×2 – 5x – 6

(a) straight line	(b) parabolic
(c) circular	(d) None of these

Answer: (b) parabolic

(ii) The expression of the polynomial represented by the graph is

(a) x -49

(b) x -64

(c) x -36

(d) x -81

Answer: (c) x2-36

(iii) Find the value of the polynomial represented by the graph when x = 6.

(a) -2

(b) -1

(c) 0

(d) 1

Answer: (c) 0

(iv) The sum of zeroes of the polynomial x 2  + 2x – 3 is

(a) -1

(b) -2

(c) 2

(d) 1

Answer: (b) -2

(v) If the sum of zeroes of polynomial at 2  + 5t + 3a is equal to their product, then find the value of a.

(a) -5

(b) -3

(c) 53

(d) −53

Answer:  (d) −53

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 2 Polynomials with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Polynomials Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Case Study Based Questions for Class 10 Maths Chapter 2 Polynomials

• Last modified on: 11 months ago
• Reading Time: 4 Minutes

Case Study Questions for Class 10 Maths Chapter 1 Real Numbers

Question 1:

Priya and her husband Aman who is an architect by profession, visited France. They went to see Mont Blanc Tunnel which is a highway tunnel between France and Italy, under the Mont Blanc Mountain in the Alps, and has a parabolic cross-section. The mathematical representation of the tunnel is shown in the graph.

Based on the above information, answer the following questions.

(1) The zeroes of the polynomial whose graph is given, are (a) -2, 8 (b)-2, -8 (c) 2,8 (d) -2,0

(2) What will be the expression of the polynomial given in diagram? (a) x 2 – 6x + 16 (b) -x 2 + 6x + 16 (c) x 2 + 6x + 16 (d) -x 2 – 6x – 16

(3) What is the value of the polynomial. represented by the graph, when x = 4? (a) 22 (b) 23 (c) 24 (d) 25

(4) If the tunnel is represented by -x 2 +3x-2. then its zeroes are (a) -1, -2 (b) 1, -2 (c) -1, 2 (d) 1, 2

(5) If one of the zero is 4 and sum of zeroes is -3, then representation of tunnel as a polynomial is (a) x 2 -x+24 (b)-x 2 -3x+28 (c) x 2 +x+28 (d) x 2 -x+28

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CBSE Case Study Questions for Class 10 Maths Polynomials Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Polynomials in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 10 Maths Polynomials PDF

Mcq set 1 -, mcq set 2 -, checkout our case study questions for other chapters.

• Chapter 1: Real Numbers Case Study Questions
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• Chapter 4: Quadratic Equation Case Study Questions
• Chapter 5: Arithmetic Progressions Case Study Questions

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Class 10 Maths Chapter 2 MCQ

Class 10 Maths Chapter 2 MCQ based on Case Study with answers and explanation for the first term exams 2024-25. All the questions including CBSE MCQ set of questions are answered with complete explanation. Class 10 Maths Chapter 2 Case study based MCQ of Polynomials helps the students to understand the pattern of CBSE question papers and way of answering.

During the skipping through skipping rope, its look like the in the form of parabola. It is a natural examples of parabolic shape which is represented by a quadratic polynomial. Similarly, we can observe in many other cases forming a in a variety of forms of different parabolas.

In the standard form of quadratic polynomial, ax² + bx + c, the condition between a, b and c are

Because if a = 0, the equation become linear. Then it is not a quadratic polynomial. Hence, the correct option is (C).

• View Answer

If the roots of the quadratic polynomial are unequal, where the discriminant D = b² – 4ac, then

We know that: If D = b² – 4ac 0, real and unequal roots. Hence, the correct option is (A).

If α and -α are the zeroes of the quadratic polynomial 2x² – 3(k – 4)x – 8, then k is

From the quadratic polynomial 2x² – 3(k – 4)x – 8 Sum of zeros = 3(k – 4)/2 [Because sum of zeros = -b/a] So, α + (- α) = 3(k – 4)/2, therefore, k – 4 = 0 or k = 4 Hence, the correct option is (A).

The graph of x² – 1 = 0

The given equation: x² – 1 = 0 or 1.x² + 0.x – 1 = 0 Here, a = 1, b = 0 and c = – 1 D = b² – 4ac = 0² – 4 х 1 х(- 1) = 4, therefore, there is two real root. So, the graph of the equation intersects x‐axis at two distinct points. Hence, the correct option is (A).

If the sum of the roots is p and product of the roots is -p, then the quadratic polynomial is

We know that the equation of a quadrilateral is given by: k [x² – (sum of roots)x + product of roots)] Therefore, the equation = k(x² – (p)x + (-p)] = k(x² – px – p) Hence, the correct option is (C).

The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

In the standard form of quadratic polynomial, ax² + bx + c, a, b and c are

Because if a = 0, the equation become linear. Then it is not a quadratic equation. Hence, the correct option is (C).

If the roots of the quadratic polynomial are equal, where the discriminant D = b² – 4ac, then

We know that: If D = b² – 4ac 0, real and unequal roots. Hence, the correct option is (D).

If α and 1/ α are the zeroes of the quadratic polynomial 2x² – x + 8k, then k is

From the quadratic polynomial 2x² – x + 8k Product of zeros = 8k/4 [Because product of zeros = c/a] So, α x (1/α) = 8k/2 Therefore, 4k = 1 Hence, k = 1/4 Hence, the correct option is (B).

The graph of x² + 1 = 0

The given equation: x² + 1 = 0 or 1.x² + 0.x + 1 = 0 Here, a = 1, b = 0 and c = 1 D = b² – 4ac = 0² – 4 х 1 х 1 = – 4, therefore, there is no real root. So, the graph of the equation neither touches nor intersects x‐axis. Hence, the correct option is (C).

If the sum of the roots is –p and product of the roots is -1/p, then the quadratic polynomial is

We know that the equation of a quadrilateral is given by: k [x² – (sum of roots)x + product of roots)] Therefore, the equation = k(x² – (-p)x + (-1/p)] = k(x² + px – 1/p) Hence, the correct option is (C).

Observe the position of the athlete taking long jump. He use to follow every time a particular shape of path. In the figure, a student can observe that the different positions can be related to representation of quadratic polynomial.

The path of the different positions form a

When we draw a dotted line following the different positions of athlete, it show a parabolic path. So, it is a parabola. Hence, the correct option is (D).

If the above case is represented by quadratic polynomial ax² + bx + c, then

If a > 0, the parabola is upward. If a < 0, the parabola is downward. Hence, the correct option is (C).

If the sum of zeros of quadratic polynomial ax² + bx + c is equal to product of zero, then

Given polynomial: ax² + bx + c Sum of zeros = -b/a, Product of zeros = c/a, According to question, -b/a = c/a Therefore, – b = a or a + b = 0 Hence, the correct option is (C).

Observe the graph given below.

In the above graph, how many zeroes are there for the polynomial?

The graph of the polynomial cutting the x-axis at four distinct points. So, it has 4 zeros. Hence, the correct option is (D).

The four zeroes in the above shown graph are

The graph of the polynomial cutting x-axis at (-4, 0), (-2, 0), (1, 0) and (3, 0). So, the zeros of polynomial are -4, -2, 1 and 3. Hence, the correct option is (A).

An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

The shape of the poses shown is

The pose shown above are in the format of parabola. Hence, the correct option is (D).

The graph of parabola opens downwards, if

The zeroes of the quadratic polynomial 4√3 x² + 5x – 2√3 are.

Given polynomial: 4√3 x² + 5x – 2√3 = 4√3 x² + 8x – 3x – 2√3 = 4x (√3x + 2) – √3 (√3x + 2) = (√3x + 2) (4x – √3) Putting (√3x + 2) (4x – √3) = 0 x = -2/√3 or x = √3/4 Hence, the correct option is (B).

Observe the following graph:

In the graph, how many zeroes are there for the polynomial?

The graph of the polynomial cutting the x-axis at two distinct points. So, it has two zeros. Hence, the correct option is (C).

The two zeroes in the above shown graph are

The graph of the polynomial cutting x-axis at (-2, 0) and (4, 0). So, the zeros of polynomial are -2 and 4. Hence, the correct option is (B).

Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.

The shape of the path traced shown is

The graph of parabola opens upwards, if.

Observe the following graph and answer:

The graph of the polynomial cutting the x-axis at three distinct points. So, it has three zeros. Hence, the correct option is (D).

The three zeroes in the above shown graph are

The graph of the polynomial cutting x-axis at (-3, 0), (-1, 0) and (2, 0). So, the zeros of polynomial are -3, -1 and 2. Hence, the correct option is (C).

What will be the expression of the polynomial?

The zeros of polynomial are -3, -1 and 2. Let α = -3, β = -1 and γ = 2 So, α + β + γ = -3 + (-1) + 2 = – 4 + 2 = -2 αβ + βγ + αγ = (-3)(-1) + (-1)(2) + (2)(-3) = 3 – 2 – 6 = – 5 αβγ = (-3)(-1)(2) = 6 Equation of polynomial = x³ – (α + β + γ) x² + (αβ + βγ + αγ) x – αβγ = x³ – (-2)x² + (- 5)x – 6 = x³ + 2x² – 5x – 6

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Case Study Class 10 Maths Questions

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Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

• Real Numbers Case Study Question
• Polynomials Case Study Question
• Pair of Linear Equations in Two Variables Case Study Question
• Quadratic Equations Case Study Question
• Arithmetic Progressions Case Study Question
• Triangles Case Study Question
• Coordinate Geometry Case Study Question
• Introduction to Trigonometry Case Study Question
• Some Applications of Trigonometry Case Study Question
• Circles Case Study Question
• Area Related to Circles Case Study Question
• Surface Areas and Volumes Case Study Question
• Statistics Case Study Question
• Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

I	NUMBER SYSTEMS	06
II	ALGEBRA	20
III	COORDINATE GEOMETRY	06
IV	GEOMETRY	15
V	TRIGONOMETRY	12
V	MENSURATION	10
VI	STATISTICS & PROBABILITY	11

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

• Find the production in the 1 st year.
• Find the production in the 12 th year.
• Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

• Find the distance between Lucknow (L) to Bhuj(B).
• If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
• Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

• Find the distance PA.
• Find the distance PB
• Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

• What is the length of the line segment joining points B and F?
• The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
• What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

• If the first circular row has 30 seats, how many seats will be there in the 10th row?
• For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
• If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

• Draw a neat labelled figure to show the above situation diagrammatically.

• What is the speed of the plane in km/hr.

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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CBSE Class 10 Maths: Case Study Questions of Chapter 2 Polynomials PDF Download

Case study Questions in the Class 10 Mathematics Chapter 2  are very important to solve for your exam. Class 10 Maths Chapter 2 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based   questions for Class 10 Maths Chapter 2  Polynomials

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Polynomials Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 2 Polynomials

Case Study/Passage-Based Questions

Question 1:

Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoors on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of a parabola representing quadratic polynomial.

1. The shape of the path traced shown is

d) Parabola

Answer: d) Parabola

2. The graph of parabola opens upwards, if _______

b) a < 0

c) a > 0

Answer: c) a > 0

3. Observe the following graph and answer

In the above graph, how many zeroes are there for the polynomial?

Answer: d) 3

4. The three zeroes in the above shown graph are

b) -2, 3, 1

c) -3, -1, 2

d) -2, -3, -1

Answer: c) -3, -1, 2

5. What will be the expression of the polynomial?

a) x 3  + 2x 2  – 5x – 6

b) x 3  + 2x 2  – 5x + 6

c) x 3  + 2x 2  + 5x – 6

d) x 3  + 2x 2  + 5x + 6

Answer: a) x3 + 2×2 – 5x – 6

(a) straight line	(b) parabolic
(c) circular	(d) None of these

Answer: (b) parabolic

(ii) The expression of the polynomial represented by the graph is

(a) x -49

(b) x -64

(c) x -36

(d) x -81

Answer: (c) x2-36

(iii) Find the value of the polynomial represented by the graph when x = 6.

(a) -2

(b) -1

(c) 0

(d) 1

Answer: (c) 0

(iv) The sum of zeroes of the polynomial x 2  + 2x – 3 is

(a) -1

(b) -2

(c) 2

(d) 1

Answer: (b) -2

(v) If the sum of zeroes of polynomial at 2  + 5t + 3a is equal to their product, then find the value of a.

(a) -5

(b) -3

(c) 53

(d) −53

Answer:  (d) −53

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 2 Polynomials with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Polynomials Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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10th Class Mathematics Polynomials Question Bank

Done case based (mcqs) - polynomials total questions - 40.

Case Study - 1 : Q. 1 to 5

The below pictures show few natural examples of parabolic shape which can be represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms. Based on the above information, answer the following questions:

A) all are real numbers done clear

B) all are rational numbers done clear

C) 'a' is a non-zero real number and b and c are any real numbers done clear

D) all are integers done clear

question_answer 2) If the roots of the quadratic polynomial are equal, and the discriminant \[D={{b}^{2}}-4ac,\] then:

A) \[D>0\] done clear

B) \[D<0\]      done clear

C) \[D\ge 0\] done clear

D) \[D=0\] done clear

question_answer 3) If \[\alpha \] and \[\frac{1}{\alpha }\]are the zeroes of the quadratic polynomial \[2{{x}^{2}}-x+8k,\] then k is:

A) \[4\] done clear

B) \[\frac{1}{4}\] done clear

C) \[\frac{-1}{4}\] done clear

D) \[2\] done clear

question_answer 4) The graph of \[{{\text{x}}^{\text{2}}}+\text{4}=0:\]

A) intersects X-axis at two distinct points done clear

B) touches X-axis at a point done clear

C) neither touches nor intersects X-axis done clear

D) either touches or intersects X-axis. done clear

question_answer 5) If the sum of the roots is \[-p\] and product of the roots \[-\frac{1}{p}\] is, then the quadratic polynomial is:

A) \[k\left( -p{{x}^{2}}+\frac{x}{p}+1 \right)\] done clear

B) \[k\left( p{{x}^{2}}-\frac{x}{p}-1 \right)\] done clear

C) \[k\left( {{x}^{2}}+px-\frac{1}{p} \right)\] done clear

D) \[k\left( {{x}^{2}}-px+\frac{1}{p} \right)\] done clear

Case Study : Q. 6 to 10

Manya is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modem yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

Based on the above information, answer the following questions:

A) spiral done clear

B) ellipse done clear

C) linear done clear

D) parabola done clear

question_answer 7) The graph of parabola opens downwards, if..........

A) \[a\ge 0\] done clear

B) \[a=0\] done clear

C) \[a<0\] done clear

D) \[a>0\] done clear

In the graph, how many zeroes are there for the polynomial?

A) 0 done clear

B) 1 done clear

C) 2 done clear

D) 3 done clear

question_answer 9) The quadratic polynomial of the two zeroes in the above shown graph are:

A) \[k({{x}^{2}}-2x-8)\] done clear

B) \[k({{x}^{2}}+2x-8)\] done clear

C) \[k({{x}^{2}}+2x+8)\] done clear

D) \[k({{x}^{2}}-2x+8)\] done clear

question_answer 10) The   zeroes   of   the   quadratic   polynomial \[4\sqrt{3}\,{{x}^{2}}+5x-2\sqrt{3}\] are:

A) \[\frac{2}{\sqrt{3}}.\frac{\sqrt{3}}{4}\] done clear

B) \[-\frac{2}{\sqrt{3}}.\frac{\sqrt{3}}{4}\] done clear

C) \[\frac{2}{\sqrt{3}}.-\frac{\sqrt{3}}{4}\] done clear

D) \[-\frac{2}{\sqrt{3}}.-\frac{\sqrt{3}}{4}\] done clear

Case Study : Q. 11 to 15
Applications   of   parabolas - highway   overpasses/ underpasses. A highway underpass is parabolic in shape.
Parabola: A parabola is the graph that results from \[p(x)=a{{x}^{2}}+bx+c\] Parabolas are symmetric about a vertical line known as the axis of symmetry.
Parabolic chamber \[y=2{{x}^{2}}/nw\]
The axis of symmetry runs through the maximum or minimum point of the parabola which is called the vertex.
Based on the above information, answer the following questions.
If the highway overpass is represented by \[{{x}^{2}}-2x-8\].
Then its zeroes are:

A) \[(2,-4)\] done clear

B) \[(4,-2)\] done clear

C) \[(-2,-2)\] done clear

D) \[(-4,-4)\] done clear

The highway overpass is represented graphically.

Zeroes of a polynomial can be expressed graphically.

Number of zeroes of polynomial is equal to number of points where the graph of polynomial:

A) Intersects X-axis done clear

B) Intersects V-axis done clear

C) Intersects /-axis or X-axis done clear

D) None of these done clear

question_answer 13) Graph of a quadratic polynomial is a:

A) straight line done clear

B) circle done clear

C) parabola done clear

D) ellipse done clear

question_answer 14) The representation of Highway Underpass whose one zero is 6 and sum of the zeroes is 0, is:

A) \[{{x}^{2}}-6x+2\] done clear

B) \[{{x}^{2}}-36\] done clear

C) \[{{x}^{2}}-6\] done clear

D) \[{{x}^{2}}-3\] done clear

question_answer 15) The number of zeroes that polynomial \[f(x)={{(x-2)}^{2}}+4\] can have is:

A) 1 done clear

B) 2 done clear

C) 0 done clear

Case Study : Q. 16 to 20

A student was given the task to prepare a graph of quadratic polynomial \[y=-8-2x+{{x}^{2}}.\]. To draw this graph he take seven values of y corresponding to different values of x. After plotting the points on the graph paper with suitable scale, he obtain the graph as shown below.

Based on the above graph, answer the following questions:

A) Parabola done clear

B) Hyperbola done clear

C) Ellipse done clear

question_answer 17) The zeroes of given quadratic polynomial are:

A) \[2,-4\] done clear

B) \[-2,4\] done clear

C) \[3,-4\] done clear

D) \[-3,4\] done clear

question_answer 18) Read from the graph the value of y corresponding to \[x=-1\] is:

A) \[-8\] done clear

B) \[-6\] done clear

C) \[-5\] done clear

D) \[-2\] done clear

question_answer 19) The graph of the given quadratic polynomial cut at which points on the X-axis?

A) \[(-2,0),\,\,(4,0)\] done clear

B) \[(0,-2),\,\,(0,4)\] done clear

C) \[(0,-2),\,\,(0,-8)\] done clear

D) \[None\,\, of\,\, the\,\,above\] done clear

question_answer 20) The graph of the given quadratic polynomial cut at which point on X-axis?

A) \[(-8,0)\] done clear

B) \[(0,-8)\] done clear

C) \[(-10,0)\] done clear

D) \[(-10,0)\] done clear

Case Study : Q. 21 to 25

In a classroom, four students Anil, Jay, Richa and Suresh were asked to draw the graph of \[p(x)=a{{x}^{2}}+bx+c\].

Following graphs are drawn by the students:

Based on the above graphs, answer the following questions:

C) 3 done clear

D) 4 done clear

question_answer 22) Which type of polynomial is represented by Jay's graph?

A) Linear done clear

B) Parabola done clear

C) Zig-zag done clear

question_answer 23) How many zeroes are there for the Richa's graph?

question_answer 24) If \[p(x)=a{{x}^{2}}+bx+c\] and \[a+b+c=0,\] then one zero is:

A) \[\frac{-b}{a}\]  done clear

B) \[\frac{c}{a}\] done clear

C) \[\frac{b}{c}\] done clear

D) \[-\frac{c}{a}\] done clear

question_answer 25) If \[p(x)=a{{x}^{2}}+bx+c\] and \[a+c=b,\] then one of the zeroes is:

A) \[\frac{b}{a}\] done clear

C) \[\frac{-c}{a}\] done clear

D) \[\frac{-b}{a}\] done clear

Case Study : Q. 26 to 30

Ramesh was asked by one of his friends to find the polynomial whose zeroes are \[\frac{-2}{\sqrt{3}}\] and \[\frac{\sqrt{3}}{4}\]. He obtained the polynomial as shown below:

Let \[\alpha =\frac{-2}{\sqrt{3}}\] and \[\alpha =\frac{\sqrt{3}}{4}\]

\[\Rightarrow \,\,\,\,\,\,\,\alpha +\beta =\frac{-2}{\sqrt{3}}+\frac{\sqrt{3}}{4}=\frac{-8+1}{4\sqrt{3}}=\frac{-7}{4\sqrt{3}}\]

\[\Rightarrow \,\,\,\,\,\,\,\alpha \beta =\frac{-2}{\sqrt{3}}\times \frac{\sqrt{3}}{4}=\frac{-1}{2}\]

Required polynomial \[={{x}^{2}}-(\alpha +\beta )x+\alpha \beta \]

\[={{x}^{2}}-\left( \frac{-7}{4\sqrt{3}} \right)x+\left( \frac{-1}{2} \right)\]

\[={{x}^{2}}+\frac{7x}{4\sqrt{3}}-\frac{1}{2}\]

\[=4\sqrt{3}{{x}^{2}}+7x-2\sqrt{3}\]

His another friend Kavita pointed out that the polynomial obtained is not correct.

Based on the above situation, answer the following questions:

A) Yes done clear

B) No done clear

C) Can't say done clear

question_answer 27) If yes, then the correct quadratic polynomial is:

A) \[4\sqrt{3}{{x}^{2}}-5x+2\sqrt{3}\] done clear

B)        \[4\sqrt{3}{{x}^{2}}+5x-2\sqrt{3}\] done clear

C) \[4\sqrt{3}{{x}^{2}}+5x+2\sqrt{3}\] done clear

D) \[4\sqrt{3}{{x}^{2}}-5x-2\sqrt{3}\] done clear

question_answer 28) The value of \[{{\alpha }^{2}}+{{\beta }^{2}}\] is:

A) \[\frac{53}{48}\] done clear

B) \[\frac{59}{48}\] done clear

C) \[\frac{73}{48}\] done clear

D) \[\frac{71}{48}\] done clear

question_answer 29) What is the value of the correct polynomial if \[x=-1\]?

A) \[-5+2\sqrt{3}\] done clear

B) \[5-2\sqrt{3}\] done clear

C) \[5-6\sqrt{3}\] done clear

D) \[-5+6\sqrt{3}\] done clear

question_answer 30) The value of \[{{\alpha }^{3}}-{{\beta }^{3}}\]is:

A) \[\frac{-539}{192\sqrt{3}}\] done clear

B) \[\frac{539}{192\sqrt{3}}\] done clear

C) \[\frac{539\sqrt{3}}{192}\] done clear

D) \[\frac{-539\sqrt{3}}{192}\] done clear

Case Study : Q. 31 to 35

A group of school friends went on an expedition to see caves. One person remarked that the entrance of the caves resembles a parabola, and can be represented by a quadratic polynomial \[f(x)=a{{x}^{2}}+bx+c,\] \[a\ne 0,\] where a, b and c are real numbers.

Based on the above information give the answer of the following questions.

A) \[\frac{3}{5}\] done clear

B) \[\frac{3}{4}\] done clear

C) \[\frac{2}{5}\] done clear

D) \[\frac{1}{5}\] done clear

question_answer 32) The zeroes of the quadratic polynomial \[{{x}^{2}}+20x+96\]are:

A) both positive done clear

B) both negative done clear

C) one positive and other negative done clear

D) both equal done clear

question_answer 33) The quadratic polynomial whose zeroes are 5 and \[-12\] is given by:

A) \[{{x}^{2}}+7x-60\] done clear

B) \[15{{x}^{2}}-x-6\] done clear

C) \[{{x}^{2}}-7x+60\] done clear

D) \[15{{x}^{2}}+x+6\] done clear

question_answer 34) If one zero of the polynomial \[f(x)=5{{x}^{2}}+13x+m\] is reciprocal of the other, then the value of m is:

A) 6 done clear

B) 0 done clear

C) 5 done clear

D) 1 done clear

question_answer 35) Which of the following cannot be the graph, of a quadratic polynomial?

Case Study : Q. 36 to 40

Naveeka everyday goes to swimming. One day, Naveeka noticed the water coming out of the pipes to fill the pool.

She then told her brother that the shape of the path of the water falling is like that of a parabola and also that a parabola can be represented by a quadratic polynomial which has atmost two zeroes.

Based on the given information, answer the following questions.

question_answer 37) If the product of the zeroes of the quadratic polynomial \[f(x)=a{{x}^{2}}-6x-6\] is 4, then the value of a is:

A) \[\frac{-3}{2}\] done clear

B) \[\frac{3}{2}\] done clear

C) \[\frac{2}{3}\] done clear

D) \[\frac{-2}{3}\] done clear

question_answer 38) The flow of the water in the pool is represented by \[{{x}^{2}}-2x-8,\] then its zeroes are:

B) \[4,-2\] done clear

C) \[2,-2\] done clear

D) \[-4,-4\] done clear

question_answer 39) If a and p be the zeroes of the polynomial \[{{x}^{2}}-1,\]then the value of \[\frac{1}{\alpha }+\frac{1}{\beta }\]is:

A) \[0\] done clear

B) \[\frac{1}{2}\] done clear

C) \[1\] done clear

D) \[-1\] done clear

question_answer 40) A quadratic polynomial whose one zero is \[-3\] and product of zeroes is 0, is:

A) \[3{{x}^{2}}+3\] done clear

B) \[{{x}^{2}}-3x\] done clear

C) \[{{x}^{2}}+3x\] done clear

D) \[3{{x}^{2}}-3\] done clear

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Chapter 2 Class 10 Polynomials

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Updated the chapter according to the new NCERT Book for 2023-24 session

Get NCERT Solutions of C hapter 2 Class 10 Polynomials free at Teachoo. All NCERT Exercise Questions, Examples and Optional Questions have been solved with video of each and every question.

In this chapter, we will learn

• What is a polynomial
• What are monomial, binomials, trinomials
• What is the degree of polynomial
• What are linear, quadratic and cubic polynomials
• What are Zeroes of a Polynomials

• How to find Zeroes of a Polynomials (both quadratic and cubic)
• Quadratic Polynomial
• Cubic Polynomial
• Dividing two polynomials, and verifying the Division Algorithm for Polynomials

We have divided this chapter into 2 parts - Serial Order Wise and Concept Wise.

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Case Based Questions Test: Polynomials - Class 10 MCQ

10 questions mcq test - case based questions test: polynomials.

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Direction: Read the following text and answer the following questions on the basis of the same: An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial. The zeroes of the quadratic polynomial

Hence, zeroes of polynomial

Direction: Read the following text and answer the following questions on the basis of the same: An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial. The graph of parabola opens downwards, if _______

Direction: read the following text and answer the following questions on the basis of the same: an asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. in the figure, one can observe that poses can be related to representation of quadratic polynomial. the two zeroes in the above shown graph are.

Zeroes are the values of x where graph intersects the x-axis

Therefore, Zeroes are -2 and 4

Direction: Read the following text and answer the following questions on the basis of the same:

An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

The shape of the poses shown is

• D. Parabola

The shape of the poses shown is Parabola.

In the graph, how many zeroes are there for the polynomial?

Therefore, Number of zeroes = 2

Applications of Parabolas: Highway Overpasses/ Underpasses

A highway underpass is parabolic in shape.

Shape of Cross Slope:

A parabola is the graph that results from p(x) = ax 2 + bx + c.

Parabolas are symmetric about a vertical line known as the Axis of Symmetry.

The Axis of Symmetry runs through the maximum or minimum point of the parabola which is called the vertex.

The number of zeroes that polynomial f(x) = (x – 2) 2 + 4 can have is:

f(x) = (x – 2) 2 + 4

= x 2 + 4 – 4x + 4

= x 2 – 4x + 8.

i.e., It has no factorisation.

Hence no real value of x is possible, i.e., no zero.

The highway overpass is represented graphically. Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial:

• A. Intersects X-axis
• B. Intersects Y-axis
• C. Intersects Y-axis or X-axis
• D. None of the above

The representation of Highway Underpass whose one zero is 6 and sum of the zeroes is 0, is:

• A. x 2 – 6x + 2
• B. x 2 – 36

If the highway overpass is represented by x 2 – 2x – 8.Then its zeroes are

• A. (2, – 4)
• B. (4, – 2)
• C. (– 2, – 2)
• D. (– 4, – 4)

or, x 2 – 4x + 2x – 8 = 0

or, x(x – 4) + 2(x – 4) = 0

or, (x – 4) (x + 2) = 0

or, x = 4, x = – 2

Graph of a quadratic polynomial is a:

• A. straight line
• C. parabola

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