Polynomials Class 10 Case Study Questions Maths Chapter 2

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Last Updated on April 2, 2025 by XAM CONTENT

Hello students, we are providing case study questions for class 10 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 10 maths. In this article, you will find case study questions for CBSE Class 10 Maths Chapter 2 Polynomials. It is a part of Case Study Questions for CBSE Class 10 Maths Series.

Chapter	Polynomials
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	10
Subject	Maths
Unit	Unit 2 Algebra
Useful for	Class 10 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 10 Maths Chapterwise Case Study

Case Study Questions on Polynomials

Questions

Passage 1:

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

Let $\quad \alpha=\frac{-2}{\sqrt{3}}$ and $\beta=\frac{\sqrt{3}}{4}$
Then, $\quad \alpha+\beta=\frac{-2}{\sqrt{3}}+\frac{\sqrt{3}}{4}=\frac{-8+1}{4 \sqrt{3}}=\frac{-7}{4 \sqrt{3}}$
and $\quad \alpha \beta=\frac{-2}{\sqrt{3}} \times \frac{\sqrt{3}}{4}=\frac{-1}{2}$

$$
\begin{aligned}
\therefore \text { Required polynomial } & =x^2-(\alpha+\beta) x+\alpha \beta \\
& =x^2-\left(\frac{-7}{4 \sqrt{3}}\right) x+\left(\frac{-1}{2}\right) \\
& =x^2+\frac{7 x}{4 \sqrt{3}}-\frac{1}{2} \\
& =4 \sqrt{3} x^2+7 x-2 \sqrt{3}
\end{aligned}
$$

His another friend Kavita pointed out that the polynomial obtained is not correct.
Based on the above information, solve the following questions:

Q 1. Is the claim of Kavita correct?
Q 2. If given polynomial is incorrect, then find the correct quadratic polynomial.
Q 3. Find the value of $\alpha^2+\beta^2$.
Q 4. What is the value of the correct polynomial, if $x=-1$ ?
Q 5. If correct polynomial $p(x)$ is a factor of $(x-2)$, then find $p(2)$.

Answers

1. Given, $\alpha=-\frac{2}{\sqrt{3}}$ and $\beta=\frac{\sqrt{3}}{4}$

$$
\therefore \quad \alpha+\beta=\frac{-2}{\sqrt{3}}+\frac{\sqrt{3}}{4}=\frac{-8+3}{4 \sqrt{3}}=\frac{-5}{4 \sqrt{3}}
$$

and $\alpha \beta=\frac{-2}{\sqrt{3}} \times \frac{\sqrt{3}}{4}=-\frac{1}{2}$
Yes, because value of $(\alpha+\beta)$ calculated by Anirudh is incorrect.

2.

$$
\begin{aligned}
\text { Required polynomial } & =k\left[x^2-(\alpha+\beta) x+\alpha \beta\right] \\
& =k\left(x^2+\frac{5 x}{4 \sqrt{3}}-\frac{1}{2}\right) \\
& =\frac{k}{4 \sqrt{3}}\left(4 \sqrt{3} x^2+5 x-2 \sqrt{3}\right) \\
& =\left(4 \sqrt{3} x^2+5 x-2 \sqrt{3}\right)
\end{aligned}
$$

where $k=4 \sqrt{3}$

3.

$$
\begin{aligned}
\alpha^2+\beta^2 & =(\alpha+\beta)^2-2 \alpha \beta \\
& =\left(\frac{-5}{4 \sqrt{3}}\right)^2-2 \times\left(\frac{-1}{2}\right)=\frac{25}{48}+1=\frac{73}{48}
\end{aligned}
$$

Alternate method:

$$
\alpha^2+\beta^2=\left(\frac{-2}{\sqrt{3}}\right)^2+\left(\frac{\sqrt{3}}{4}\right)^2=\frac{4}{3}+\frac{3}{16}=\frac{64+9}{48}=\frac{73}{48}
$$

4. Let correct polynomial be

$$
p(x)=4 \sqrt{3} x^2+5 x-2 \sqrt{3}
$$

If $x=-1$, then

$$
\begin{aligned}
p(-1) & =4 \sqrt{3}(-1)^2+5(-1)-2 \sqrt{3} \\
& =4 \sqrt{3}-5-2 \sqrt{3}=2 \sqrt{3}-5
\end{aligned}
$$

5. We have, $p(x)=4 \sqrt{3} x^2+5 x-2 \sqrt{3}$

Since, $p(x)$ is a factor of $(x-2)$, then

$$
\begin{aligned}
p(2) & =4 \sqrt{3}(2)^2+5(2)-2 \sqrt{3} \\
& =16 \sqrt{3}+10-2 \sqrt{3}=14 \sqrt{3}+10
\end{aligned}
$$

Hence, $p(2)$ is $14 \sqrt{3}+10$.

Also check

• Arithmetic Progressions Class 10 Case Study Questions Maths Chapter 5
• Quadratic Equations Class 10 Case Study Questions Maths Chapter 4
• Pair of Linear Equations in Two Variables Class 10 Case Study Questions Maths Chapter 3
• Polynomials Class 10 Case Study Questions Maths Chapter 2
• Real Numbers Class 10 Case Study Questions Maths Chapter 1

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Topics from which case study questions may be asked

• Zeros of a Polynomial
• Relationship Between Zeros and Coefficients of Quadratic Polynomials

Case study questions based on above topics may be asked.

Frequently Asked Questions (FAQs) on Polynomials Case Study