MATHEMATICS CLASS- 10
MCQ- CH-4(Quadratic Equations)
Class 10 Mathematics
Chapter 4: Quadratic Equations
MCQs with Answers and Solutions
Q1. Which of the following is a quadratic equation?
(a) x + 5 = 0
(b) x² + 3x + 2 = 0
(c) x³ + 2x = 0
(d) 2/x + 1 = 0
Answer: (b) x² + 3x + 2 = 0
Solution: The highest power of x is 2.
Q2. The roots of x² − 5x + 6 = 0 are
(a) 1, 6
(b) 2, 3
(c) -2, -3
(d) 5, 6
Answer: (b) 2, 3
Solution: x² − 5x + 6 = (x − 2)(x − 3).
Q3. The standard form of a quadratic equation is
(a) ax + b = 0
(b) ax² + bx + c = 0
(c) ax³ + bx² + c = 0
(d) ax² + b = 0
Answer: (b) ax² + bx + c = 0
Q4. The value of the discriminant of x² − 4x + 4 = 0 is
(a) 16
(b) 0
(c) 4
(d) -4
Answer: (b) 0
Solution: D = b² − 4ac = (-4)² − 4(1)(4) = 0.
Q5. If D > 0, the quadratic equation has
(a) No real roots
(b) Equal roots
(c) Two distinct real roots
(d) One root
Answer: (c) Two distinct real roots
Q6. If D = 0, the roots are
(a) Imaginary
(b) Equal
(c) Distinct
(d) Irrational
Answer: (b) Equal
Q7. If D < 0, the quadratic equation has
(a) Equal roots
(b) Distinct real roots
(c) No real roots
(d) One real root
Answer: (c) No real roots
Q8. The roots of x² − 9 = 0 are
(a) ±9
(b) ±3
(c) 3 only
(d) -3 only
Answer: (b) ±3
Solution: x² = 9 ⇒ x = ±3.
Q9. The sum of roots of x² − 7x + 10 = 0 is
(a) 7
(b) -7
(c) 10
(d) -10
Answer: (a) 7
Solution: Sum = -b/a = 7.
Q10. Product of roots of x² − 7x + 10 = 0 is
(a) 7
(b) 10
(c) -10
(d) -7
Answer: (b) 10
Q11. The roots of x² − 2x − 15 = 0 are
(a) 3, 5
(b) -3, -5
(c) 5, -3
(d) 15, 1
Answer: (c) 5, -3
Solution: (x − 5)(x + 3) = 0.
Q12. The quadratic formula is
(a) (-b ± √(b² − 4ac))/2a
(b) (b ± √(b² − 4ac))/2a
(c) (-b ± √(b² + 4ac))/2a
(d) (b ± √(b² + 4ac))/2a
Answer: (a)
Q13. The roots of x² − 6x + 9 = 0 are
(a) 3, 3
(b) -3, -3
(c) 3, -3
(d) 9, 1
Answer: (a) 3, 3
Solution: (x − 3)² = 0.
Q14. The discriminant of x² + 4x + 5 = 0 is
(a) 4
(b) 0
(c) -4
(d) 16
Answer: (c) -4
Q15. Which equation has equal roots?
(a) x² − 4x + 4 = 0
(b) x² − 5x + 6 = 0
(c) x² + x + 1 = 0
(d) x² − 1 = 0
Answer: (a)
Q16. The roots of 2x² − 8x = 0 are
(a) 0, 4
(b) 4, 8
(c) 2, 4
(d) 0, 8
Answer: (a)
Solution: 2x(x − 4) = 0.
Q17. The equation x² = 49 has roots
(a) 49, -49
(b) 7, -7
(c) 7 only
(d) -7 only
Answer: (b)
Q18. The sum of roots of 2x² + 5x − 3 = 0 is
(a) -5/2
(b) 5/2
(c) -3/2
(d) 3/2
Answer: (a)
Q19. Product of roots of 2x² + 5x − 3 = 0 is
(a) -3/2
(b) 3/2
(c) -5/2
(d) 5/2
Answer: (a)
Q20. The roots of x² + 5x + 6 = 0 are
(a) 2, 3
(b) -2, -3
(c) -2, 3
(d) 2, -3
Answer: (b)
Q21. Which of the following has no real roots?
(a) x² − 1 = 0
(b) x² + 1 = 0
(c) x² − 4 = 0
(d) x² − 9 = 0
Answer: (b)
Q22. The roots of x² − 11x + 30 = 0 are
(a) 5, 6
(b) 3, 10
(c) 2, 15
(d) 1, 30
Answer: (a)
Q23. If one root of x² − 13x + 40 = 0 is 5, the other root is
(a) 7
(b) 8
(c) 9
(d) 10
Answer: (b)
Q24. The roots of x² − x − 20 = 0 are
(a) 5, -4
(b) 4, -5
(c) 2, -10
(d) 10, -2
Answer: (a)
Q25. The discriminant of x² − 8x + 15 = 0 is
(a) 4
(b) 16
(c) 25
(d) 36
Answer: (a)
Q26. (CBSE PYQ) If one root of x² + px + 12 = 0 is 3, then p equals
(a) -7
(b) 7
(c) -5
(d) 5
Answer: (a)
Solution: Other root = 4. Sum = -p = 7 ⇒ p = -7.
Q27. Which equation has roots 2 and 7?
(a) x² − 9x + 14 = 0
(b) x² + 9x + 14 = 0
(c) x² − 14x + 9 = 0
(d) x² + 14x + 9 = 0
Answer: (a)
Q28. The roots of x² − 3x = 0 are
(a) 0, 3
(b) 3, 3
(c) 0, -3
(d) 1, 3
Answer: (a)
Q29. A quadratic equation can have maximum
(a) 1 root
(b) 2 roots
(c) 3 roots
(d) 4 roots
Answer: (b)
Q30. The roots of x² − 16 = 0 are
(a) ±4
(b) ±8
(c) 4 only
(d) -4 only
Answer: (a)
Q31. The equation x² + 6x + 9 = 0 has
(a) Distinct roots
(b) Equal roots
(c) No roots
(d) Imaginary roots
Answer: (b)
Q32. The discriminant of 3x² − 12x + 12 = 0 is
(a) 0
(b) 12
(c) 24
(d) 36
Answer: (a)
Q33. If α and β are roots of x² − 9x + 20 = 0, then α + β equals
(a) 20
(b) 9
(c) -9
(d) -20
Answer: (b)
Q34. If α and β are roots of x² − 9x + 20 = 0, then αβ equals
(a) 9
(b) -9
(c) 20
(d) -20
Answer: (c)
Q35. The roots of x² + 7x + 10 = 0 are
(a) -5, -2
(b) 5, 2
(c) -5, 2
(d) 5, -2
Answer: (a)
Q36. (CBSE PYQ) If roots of x² − kx + 16 = 0 are equal, then k equals
(a) 4
(b) 8
(c) ±8
(d) ±4
Answer: (c)
Solution: D = 0 ⇒ k² − 64 = 0 ⇒ k = ±8.
Q37. Which equation has roots -4 and -5?
(a) x² + 9x + 20 = 0
(b) x² − 9x + 20 = 0
(c) x² + 20x + 9 = 0
(d) x² − 20x + 9 = 0
Answer: (a)
Q38. The value of D for x² + 2x + 10 = 0 is
(a) 36
(b) 4
(c) -36
(d) -4
Answer: (c)
Q39. The roots of x² − 25 = 0 are
(a) ±5
(b) ±25
(c) 5 only
(d) -5 only
Answer: (a)
Q40. The equation x² + 4x + 4 = 0 has root
(a) 4
(b) -4
(c) -2
(d) 2
Answer: (c)
Q41. A rectangular garden has length 3 m more than breadth. Area is 40 m². The quadratic equation formed is
(a) x² + 3x − 40 = 0
(b) x² − 3x − 40 = 0
(c) x² + 40x + 3 = 0
(d) x² − 40x + 3 = 0
Answer: (a)
Q42. (CBSE PYQ) The roots of 6x² − x − 2 = 0 are
(a) 2/3, -1/2
(b) -2/3, 1/2
(c) 1/3, -2
(d) -1/3, 2
Answer: (a)
Q43. The equation x² = 0 has
(a) Two distinct roots
(b) One repeated root
(c) No root
(d) Infinite roots
Answer: (b)
Q44. If roots are 4 and 6, then the quadratic equation is
(a) x² − 10x + 24 = 0
(b) x² + 10x + 24 = 0
(c) x² − 24x + 10 = 0
(d) x² + 24x + 10 = 0
Answer: (a)
Q45. Which of the following has irrational roots?
(a) x² − 4 = 0
(b) x² − 2 = 0
(c) x² − 9 = 0
(d) x² − 16 = 0
Answer: (b)
Q46. Sum of roots of x² + 8x + 15 = 0 is
(a) -8
(b) 8
(c) 15
(d) -15
Answer: (a)
Q47. Product of roots of x² + 8x + 15 = 0 is
(a) -8
(b) 8
(c) 15
(d) -15
Answer: (c)
Q48. If D = 49, then roots are
(a) Equal
(b) Distinct Real
(c) Imaginary
(d) Not Real
Answer: (b)
Q49. Which of the following is not a quadratic equation?
(a) x² + 2x + 1 = 0
(b) 2x² − 5 = 0
(c) x(x + 2) = 0
(d) x³ + x = 0
Answer: (d)
Q50. Which statement is true?
(a) Every quadratic equation has equal roots.
(b) Every quadratic equation has two real roots.
(c) A quadratic equation may have no real roots.
(d) A quadratic equation has only one root.
Answer: (c) A quadratic equation may have no real roots.
Solution: When the discriminant is negative, the equation has no real roots.