Preparing for Class 10 Maths Board Exam? Chapter 2 Polynomials is one of the most important chapters that frequently appears in exams. In this post, we have compiled important questions, MCQs, case study-based questions, and previous exam-level problems to help you score high.

Before attempting these questions, make sure you have practiced concepts from our detailed guides like Real Numbers MCQs, Statistics Important Questions, and Probability Practice Questions to strengthen your overall Maths preparation.

Section A: MCQs

1. The number of polynomials having −2 and 5 as zeroes is:
   (a) Exactly 1
   (b) Only 2
   (c) At most 2
   (d) Infinitely many
2. If one zero of the polynomial $x^2 – 3kx + 4k$ is twice the other, then the value of k is:
   (a) 2
   (b) −2
   (c) 1/2
   (d) −1/2
3. If α and β are the zeroes of the polynomial $ax^2 – 5x + c$ and α + β = αβ = 10, then:
   (a) a = 5, c = 1/2
   (b) a = 1, c = 5/2
   (c) a = 5/2, c = 1
   (d) a = 1/2, c = 5
4. If one zero of the polynomial $6x^2 + 37x – (k – 2)$ is reciprocal of the other, then k =
   (a) −4
   (b) 6
   (c) −6
   (d) 4
5. If α and β are zeroes of $x^2 + x – 1$, then $\frac{1}{\alpha} + \frac{1}{\beta} =$
   (a) 1
   (b) −1
   (c) 0
   (d) None
6. A quadratic polynomial whose sum of zeroes is 0 and one zero is 3, is:
   (a) $x^2 – 9$
   (b) $x^2 + 9$
   (c) $x^2 + 3$
   (d) $x^2 – 3$
7. If α and β are zeroes of $x^2 – ax – b$, then α² + β² =
   (a) $a^2 – 2b$
   (b) $a^2 + 2b$
   (c) $b^2 – 2a$
   (d) $b^2 + 2a$
8. The zeroes of $x^2 – 3x – m(m+3)$ are:
   (a) m, m+3
   (b) −m, m+3
   (c) m, −(m+3)
   (d) −m, −(m+3)

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🔹 Section B: Short Answer Questions

9. If the quadratic polynomial $ax^2 + bx + c$ has 2 same zeroes with opposite signs, find b.
10. If one zero of a quadratic polynomial $ax^2 + bx + c$ is zero, find c.
11. What constant should be added to $x^2 + 7x + 5$x2+7x+5 so that −2 is a zero?
12. Find zeroes of $x^2 + 7x + 12$x2+7x+12 and verify relations.
13. If 2 and 1/2 are zeroes of $px^2 + 5x + r$, find p and r.
14. If α, β are zeroes of $x^2 – x – 2$, find polynomial with zeroes $2α+1, 2β+1$.
15. If α, β are zeroes of $3x^2 – 4x + 1$, find polynomial with zeroes $a^2/b, b^2/a$.

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🔹 Section C: Long Answer Questions

16. Find k such that sum of zeroes equals half their product for $x^2 – (k+6)x + 2(2k-1)$.
17. If α, β are zeroes of $x^2 – 4x + 3$, find $α^4β^2 + α^2β^4$.
18. Find quadratic polynomial if α+β = 24 and α−β = 8.
19. Find k if $2x^2 + 5x + k$ satisfies $α^2 + β^2 + αβ = 21/4$.
20. If one zero is negative of other in $14x^2 – 42kx – 9$, find k.

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To strengthen your preparation, also practice related chapters like Pair of Linear Equations, Quadratic Equations, and Arithmetic Progressions, as these chapters are interconnected and frequently asked together in CBSE exams.

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❓ FAQs

Q1. What is a polynomial?

A polynomial is an algebraic expression consisting of variables and coefficients.

Q2. How many zeroes can a quadratic polynomial have?

A quadratic polynomial can have at most 2 zeroes.

Q3. What is the relation between zeroes and coefficients?

For $ax^2 + bx + c$ax2+bx+c:
Sum = −b/a, Product = c/a

Q4. Are case study questions important?

Yes, they are very important for CBSE board exams.

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✅ Answers

1. (d)
2. (c)
3. (c)
4. (b)
5. (b)
6. (a)
7. (b)
8. (c)
9. b = 0
10. c = 0
11. 7
12. −3, −4 (Verified)
13. p = 1, r = 2
14. Required polynomial: $x^2 – 4x + 3$x2−4x+3
15. Solve → polynomial obtained
16. k = 2
17. 9
18. $x^2 – 24x + 128$x2−24x+128
19. k = 2
20. k = 0

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🔚 Conclusion (with Internal Linking)

To score full marks in Class 10 Maths, mastering Polynomials is essential. Make sure you also revise topics like Statistics, Probability, and Real Numbers regularly. Practice consistently and solve previous year questions to boost your confidence.