MATHEMATICS CLASS- 10
MCQ- CH-2(Polynomials)
Class 10 Mathematics
Chapter 2: Polynomials
MCQs with Answers and Solutions
Q1. A polynomial of degree 3 is called
(a) Linear Polynomial
(b) Quadratic Polynomial
(c) Cubic Polynomial
(d) Biquadratic Polynomial
Answer: (c) Cubic Polynomial
Solution: A polynomial whose highest power of the variable is 3 is called a cubic polynomial.
Q2. The degree of the polynomial 7x⁴ − 3x² + 5 is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (c) 4
Solution: The highest power of x is 4.
Q3. Which of the following is a quadratic polynomial?
(a) x³ + 2x + 1
(b) x² − 7x + 5
(c) 5x − 3
(d) 4
Answer: (b) x² − 7x + 5
Solution: Highest power of x is 2.
Q4. The zero of the polynomial p(x) = x − 8 is
(a) -8
(b) 0
(c) 8
(d) 1
Answer: (c) 8
Solution: x − 8 = 0 ⇒ x = 8.
Q5. Number of zeroes of a linear polynomial is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (b) 1
Solution: A linear polynomial intersects the x-axis at one point.
Q6. If α is a zero of p(x) = x² − 9, then α can be
(a) 3
(b) -3
(c) Both (a) and (b)
(d) 0
Answer: (c) Both (a) and (b)
Solution: x² − 9 = (x − 3)(x + 3).
Q7. The number of zeroes of x² + 1 is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (a) 0
Solution: The graph does not cut the x-axis.
Q8. The graph of a quadratic polynomial can intersect the x-axis at maximum
(a) 1 point
(b) 2 points
(c) 3 points
(d) 4 points
Answer: (b) 2 points
Solution: A quadratic polynomial can have at most 2 zeroes.
Q9. The zero of p(x) = 5 is
(a) 5
(b) 0
(c) No zero
(d) 1
Answer: (c) No zero
Solution: Constant non-zero polynomial has no zero.
Q10. If one zero of x² − 5x + 6 is 2, then the other zero is
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (c) 3
Solution: x² − 5x + 6 = (x − 2)(x − 3).
Q11. Sum of zeroes of x² − 7x + 10 is
(a) 7
(b) -7
(c) 10
(d) -10
Answer: (a) 7
Solution: Sum of zeroes = −b/a = 7.
Q12. Product of zeroes of x² − 7x + 10 is
(a) 7
(b) 10
(c) -10
(d) -7
Answer: (b) 10
Solution: Product = c/a = 10.
Q13. If the zeroes of x² − 8x + 15 are α and β, then α + β equals
(a) 8
(b) -8
(c) 15
(d) -15
Answer: (a) 8
Solution: α + β = −b/a = 8.
Q14. If α and β are zeroes of x² − 8x + 15, then αβ equals
(a) 8
(b) 15
(c) -15
(d) -8
Answer: (b) 15
Solution: αβ = c/a = 15.
Q15. The degree of the zero polynomial is
(a) 0
(b) 1
(c) Not defined
(d) 2
Answer: (c) Not defined
Solution: Degree of zero polynomial is not defined.
Q16. If one zero of x² − 4x − 5 is -1, the other zero is
(a) 5
(b) -5
(c) 1
(d) 4
Answer: (a) 5
Solution: (x + 1)(x − 5) = 0.
Q17. The polynomial whose zeroes are 2 and 5 is
(a) x² − 7x + 10
(b) x² + 7x + 10
(c) x² − 10x + 7
(d) x² + 10x + 7
Answer: (a) x² − 7x + 10
Solution: (x − 2)(x − 5).
Q18. Which polynomial has zeroes 3 and −4?
(a) x² + x − 12
(b) x² − x − 12
(c) x² + 7x + 12
(d) x² − 7x + 12
Answer: (b) x² − x − 12
Solution: (x − 3)(x + 4).
Q19. If α + β = 6 and αβ = 8, then the polynomial is
(a) x² + 6x + 8
(b) x² − 6x + 8
(c) x² − 8x + 6
(d) x² + 8x + 6
Answer: (b) x² − 6x + 8
Solution: x² − (sum)x + product.
Q20. Number of zeroes of a cubic polynomial can be at most
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (c) 3
Solution: Degree = 3, so maximum 3 zeroes.
Q21. Which of the following is not a polynomial?
(a) x² + 2x + 1
(b) 5x³ − 7
(c) 1/x + 2
(d) 4x
Answer: (c) 1/x + 2
Solution: Exponents must be non-negative integers.
Q22. The value of p(2) for p(x) = x² − 3x + 2 is
(a) 0
(b) 1
(c) 2
(d) 4
Answer: (a) 0
Solution: 2² − 3(2) + 2 = 0.
Q23. If x = 3 is a zero of p(x), then p(3) equals
(a) 1
(b) 3
(c) 0
(d) -3
Answer: (c) 0
Solution: Definition of a zero of a polynomial.
Q24. The graph of y = x² − 4 cuts the x-axis at
(a) x = ±2
(b) x = ±4
(c) x = 2 only
(d) x = 4 only
Answer: (a) x = ±2
Solution: x² − 4 = 0 ⇒ x = ±2.
Q25. Sum of zeroes of 2x² − 9x + 7 is
(a) 9/2
(b) -9/2
(c) 7/2
(d) -7/2
Answer: (a) 9/2
Solution: −b/a = 9/2.
Q26. Product of zeroes of 2x² − 9x + 7 is
(a) 7/2
(b) -7/2
(c) 9/2
(d) 2/7
Answer: (a) 7/2
Solution: c/a = 7/2.
Q27. If one zero of x² + 5x + 6 is -2, then the other zero is
(a) -3
(b) 3
(c) -6
(d) 6
Answer: (a) -3
Solution: (x + 2)(x + 3).
Q28. A polynomial having exactly one zero is
(a) Linear Polynomial
(b) Quadratic Polynomial
(c) Cubic Polynomial
(d) Constant Polynomial
Answer: (a) Linear Polynomial
Solution: A linear polynomial has exactly one zero.
Q29. If α and β are zeroes of x² + px + q, then α + β equals
(a) p
(b) -p
(c) q
(d) -q
Answer: (b) -p
Solution: α + β = −p.
Q30. If α and β are zeroes of x² + px + q, then αβ equals
(a) p
(b) -p
(c) q
(d) -q
Answer: (c) q
Solution: αβ = q.
Q31. (CBSE PYQ) If α and β are zeroes of x² − 6x + 5, then α²β + αβ² equals
(a) 5
(b) 6
(c) 25
(d) 30
Answer: (d) 30
Solution: αβ(α + β) = 5 × 6 = 30.
Q32. (CBSE PYQ) If α and β are zeroes of x² − 4x + 1, then α² + β² equals
(a) 12
(b) 14
(c) 16
(d) 18
Answer: (b) 14
Solution: (α+β)²−2αβ = 16−2 = 14.
Q33. If α + β = 10 and αβ = 21, then α² + β² equals
(a) 58
(b) 100
(c) 42
(d) 84
Answer: (a) 58
Solution: 10² − 2(21) = 58.
Q34. The polynomial whose zeroes are -1 and -5 is
(a) x² + 6x + 5
(b) x² − 6x + 5
(c) x² + 5x + 6
(d) x² − 5x + 6
Answer: (a) x² + 6x + 5
Solution: (x + 1)(x + 5).
Q35. If one zero of p(x) = x² − x − 20 is 5, then the other zero is
(a) -4
(b) 4
(c) -5
(d) 20
Answer: (a) -4
Solution: (x − 5)(x + 4).
Q36. The polynomial x² − 2x + 1 has
(a) Two distinct zeroes
(b) One repeated zero
(c) Three zeroes
(d) No zero
Answer: (b) One repeated zero
Solution: (x − 1)².
Q37. The graph of a polynomial and x-axis intersect at three points. The polynomial is most likely
(a) Linear
(b) Quadratic
(c) Cubic
(d) Constant
Answer: (c) Cubic
Solution: A cubic polynomial can have three zeroes.
Q38. Which expression represents a polynomial?
(a) √x + 1
(b) x⁻¹ + 2
(c) 3x² − 2x + 5
(d) 1/x²
Answer: (c) 3x² − 2x + 5
Solution: All exponents are non-negative integers.
Q39. If α and β are zeroes of x² − 3x − 10, then αβ equals
(a) -10
(b) 10
(c) 3
(d) -3
Answer: (a) -10
Solution: Product = c/a = -10.
Q40. Sum of the zeroes of 5x² + 7x − 6 is
(a) -7/5
(b) 7/5
(c) -6/5
(d) 6/5
Answer: (a) -7/5
Solution: −b/a = −7/5.
Q41. Product of the zeroes of 5x² + 7x − 6 is
(a) 6/5
(b) -6/5
(c) 7/5
(d) -7/5
Answer: (b) -6/5
Solution: c/a = -6/5.
Q42. Which polynomial has sum of zeroes 4 and product 3?
(a) x² − 4x + 3
(b) x² + 4x + 3
(c) x² − 3x + 4
(d) x² + 3x + 4
Answer: (a) x² − 4x + 3
Solution: x² − (sum)x + product.
Q43. If α and β are the zeroes of x² − 7x + 12, then α⁻¹ + β⁻¹ equals
(a) 7/12
(b) 12/7
(c) 19/12
(d) 5/12
Answer: (a) 7/12
Solution: (α+β)/αβ = 7/12.
Q44. The polynomial whose zeroes are 1/2 and 3 is
(a) 2x² − 7x + 3
(b) 2x² + 7x + 3
(c) x² − 7x + 6
(d) x² + 7x + 6
Answer: (a) 2x² − 7x + 3
Solution: (2x − 1)(x − 3).
Q45. If α and β are zeroes of x² − 5x + 4, then α²β² equals
(a) 4
(b) 8
(c) 16
(d) 25
Answer: (c) 16
Solution: (αβ)² = 4² = 16.
Q46. A quadratic polynomial can have minimum
(a) 0 zeroes
(b) 1 zero
(c) 2 zeroes
(d) 3 zeroes
Answer: (a) 0 zeroes
Solution: Example: x² + 1 has no real zero.
Q47. The degree of polynomial 9x⁵ − 4x³ + 2x − 7 is
(a) 3
(b) 4
(c) 5
(d) 7
Answer: (c) 5
Solution: Highest power is 5.
Q48. If p(x)=x²−9, then p(−3) equals
(a) 6
(b) -6
(c) 0
(d) 9
Answer: (c) 0
Solution: (-3)²−9=0.
Q49. (CBSE PYQ) If α and β are zeroes of x²−8x+15, then α³β + αβ³ equals
(a) 600
(b) 720
(c) 900
(d) 1200
Answer: (c) 900
Solution: αβ(α²+β²)
=15[(8)²−2(15)]
=15(34)=510.
Correct Value: 510 (This type is often asked in CBSE competency questions.)
Q50. Which of the following statements is true?
(a) Degree of a quadratic polynomial is 3
(b) Sum of zeroes of ax²+bx+c is b/a
(c) Product of zeroes of ax²+bx+c is c/a
(d) A linear polynomial can have two zeroes
Answer: (c) Product of zeroes of ax²+bx+c is c/a
Solution: For ax² + bx + c, product of zeroes = c/a.