Class 10 Maths Chapter 2 Polynomials MCQs: Very Important

1. If one zero of the polynomial p(x) = 2x² – 7x + 3 is 3, what is the other zero?

A) 1/2
B) 3/2
C) -1
D) -3

Answer: B) 3/2

Explanation: Using the relation (Sum of zeros = 7/2), we get the other zero as 3/2.

2. The degree of the polynomial 5x⁴ – 3x³ + 2 is:

A) 4
B) 3
C) 2
D) 1

Answer: A) 4

Explanation: The highest power of x is 4, so the degree is 4.

3. The zero of the polynomial p(x) = x – 5 is:

A) 5
B) -5
C) 1
D) 0

Answer: A) 5

Explanation: Setting x – 5 = 0, we get x = 5 as the zero.

4. The polynomial x² – 5x + 6 has:

A) One real root
B) No real roots
C) Two distinct real roots
D) Infinite roots

Answer: C) Two distinct real roots

Explanation: Factorizing gives (x – 2)(x – 3) = 0, so x = 2 and x = 3 are the roots.

5. The value of k if x = 2 is a root of the polynomial p(x) = x² – kx + 3 is:

A) 3
B) 4
C) 6
D) 5

Answer: C) 6

Explanation: Substitute x = 2, so 4 – 2k + 3 = 0; solving gives k = 6.

6. If α and β are the zeros of the polynomial p(x) = x² – 5x + 6, then α + β equals:

A) -5
B) 5
C) 6
D) 1

Answer: B) 5

Explanation: Sum of zeros α + β = -coefficient of x / coefficient of x² = 5.

7. Which of the following is a quadratic polynomial?

A) 3x + 4
B) x² – 4x + 3
C) x³ + 2
D) 2x

Answer: B) x² – 4x + 3

Explanation: A quadratic polynomial has a degree of 2.

8. The product of the zeros of the polynomial p(x) = 2x² – 3x + 1 is:

A) 1/2
B) 2
C) -3
D) 1

Answer: A) 1/2

Explanation: Product of zeros = constant term / coefficient of x² = 1/2.

9. A polynomial of degree 0 is called:

A) Linear
B) Quadratic
C) Constant
D) Cubic

Answer: C) Constant

Explanation: Polynomials of degree 0 are constant as they do not contain x.

10. If the zero of the polynomial x² + kx + 6 is -2, then k is:

A) -4
B) 4
C) -6
D) 6

Answer: B) 4

Explanation: Substitute x = -2, so 4 – 2k + 6 = 0; solving gives k = 4.

11. If α and β are the zeros of the polynomial p(x) = x² + 6x + 8, then αβ equals:

A) 6
B) 8
C) -8
D) -6

Answer: B) 8

Explanation: Product of zeros αβ = constant term / coefficient of x² = 8.

12. For the polynomial p(x) = x² – 4x + 4, the sum and product of its zeros are:

A) 4 and 4
B) -4 and 4
C) 2 and 4
D) 4 and 2

Answer: A) 4 and 4

Explanation: Sum of zeros = 4, Product of zeros = 4 for x² – 4x + 4.

13. The polynomial x³ – 3x² + 3x – 1 has:

A) One zero
B) Two zeros
C) Three zeros
D) No zeros

Answer: C) Three zeros

Explanation: A cubic polynomial (degree 3) has exactly three zeros.

14. Which of the following polynomial expressions represents a linear polynomial?

A) x³ – 2
B) 5x + 1
C) x² – x
D) x – x² + 3

Answer: B) 5x + 1

Explanation: A linear polynomial has degree 1, which is seen in 5x + 1.

15. The sum of the zeros of the polynomial x² – 9x + 20 is:

A) 9
B) -9
C) 20
D) -20

Answer: A) 9

Explanation: Sum of zeros = -coefficient of x / coefficient of x² = 9.

16. The polynomial 4x² – 12x + 9 has a zero equal to:

A) 3
B) -3
C) 3/2
D) -3/2

Answer: C) 3/2

Explanation: Factoring gives (2x – 3)², so x = 3/2 is the zero.

17. The zeros of the polynomial x² – 1 are:

A) ±1
B) 1 and 0
C) 0 and -1
D) ±2

Answer: A) ±1

Explanation: Factoring x² – 1 gives (x + 1)(x – 1) = 0, so x = ±1.

18. Which of these has a degree of 1?

A) 3x² – 5x
B) 7x – 8
C) x³ + 2x
D) 4x² – x + 1

Answer: B) 7x – 8

Explanation: Degree of 7x – 8 is 1, making it a linear polynomial.

19. If α and β are the zeros of x² – 4, then αβ is:

A) -4
B) 4
C) 0
D) 2

Answer: B) 4

Explanation: Product of zeros αβ = constant term (4) / coefficient of x² = 4.

20. The value of k for which x = -3 is a zero of the polynomial x² + kx + 12 is:

A) 6
B) -6
C) 4
D) -4

Answer: A) 6

Explanation: Substitute x = -3, giving 9 – 3k + 12 = 0; solving gives k = 6.