## MCQ Questions for Class 10 Maths Quadratic Equations with Answers

1. Which of the following is not a quadratic equation

(a) x² + 3x – 5 = 0

(b) x² + x3 + 2 = 0

(c) 3 + x + x² = 0

(d) x² – 9 = 0

Answer: b

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2. The quadratic equation has degree

(a) 0

(b) 1

(c) 2

(d) 3

Answer: c

3. The cubic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

Answer: c

4. A bi-quadratic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

Answer: d

5. The polynomial equation x (x + 1) + 8 = (x + 2) {x – 2) is

(a) linear equation

(b) quadratic equation

(c) cubic equation

(d) bi-quadratic equation

Answer: a

6. The equation (x – 2)² + 1 = 2x – 3 is a

(a) linear equation

(b) quadratic equation

(c) cubic equation

(d) bi-quadratic equation

Answer: b

7. The roots of the quadratic equation 6x² – x – 2 = 0 are

Answer: c

8. The quadratic equation whose roots are 1 and

(a) 2x² + x – 1 = 0

(b) 2x² – x – 1 = 0

(c) 2x² + x + 1 = 0

(d) 2x² – x + 1 = 0

Answer: b

9. The quadratic equation whose one rational root is 3 + √2 is

(a) x² – 7x + 5 = 0

(b) x² + 7x + 6 = 0

(c) x² – 7x + 6 = 0

(d) x² – 6x + 7 = 0

Answer: d

10. The equation 2x² + kx + 3 = 0 has two equal roots, then the value of k is

(a) ±√6

(b) ± 4

(c) ±3√2

(d) ±2√6

Answer: d

11. The roots of the quadratic equation x+1x=3, x ≠ 0 are.

Answer: c

12. The roots of the quadratic equation 2x² – 2√2x + 1 = 0 are

Answer: c

13. The sum of the roots of the quadratic equation 3×2 – 9x + 5 = 0 is

(a) 3

(b) 6

(c) -3

(d) 2

Answer: c

14. If the roots of ax2 + bx + c = 0 are in the ratio m : n, then

(a) mna² = (m + n) c²

(b) mnb² = (m + n) ac

(c) mn b² = (m + n)² ac

(d) mnb² = (m – n)² ac

Answer: c

15. If one root of the equation x² + px + 12 = 0 is 4, while the equation x² + px + q = 0 has equal roots, the value of q is

Answer: a

16. a and p are the roots of 4x² + 3x + 7 = 0, then the value of 1α+1β is

Answer: b

17. If a, p are the roots of the equation (x – a) (x – b) + c = 0, then the roots of the equation (x – a) (x – P) = c are

(a) a, b

(b) a, c

(c) b, c

(d) none of these

Answer: a

18. Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are

(a) 9,1

(b) -9,1

(c) 9, -1

(d) -9, -1

Answer: a

19. If a and p are the roots of the equation 2x² – 3x – 6 = 0. The equation whose roots are 1α and 1β is

(a) 6x² – 3x + 2 = 0

(b) 6x² + 3x – 2 = 0

(c) 6x² – 3x – 2 = 0

(d) x² + 3x-2 = 0

Answer: b

20. If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then

(a) P = 0

(b) p = -2

(c) p = ±2

(d) p = 2

Answer: d

21. If one root of the quadratic equation 2x² + kx – 6 = 0 is 2, the value of k is

(a) 1

(b) -1

(c) 2

(d) -2

Answer: b

22. The roots of the quadratic equation

(a) a, b

(b) -a, b

(c) a, -b

(d) -a, -b

Answer: d

23. The roots of the equation 7x² + x – 1 = 0 are

(a) real and distinct

(b) real and equal

(c) not real

(d) none of these

Answer: a

24. The equation 12x² + 4kx + 3 = 0 has real and equal roots, if

(a) k = ±3

(b) k = ±9

(c) k = 4

(d) k = ±2

Answer: a

25. If -5 is a root of the quadratic equation 2x² + px – 15 = 0, then

(a) p = 3

(b) p = 5

(c) p = 7

(d) p = 1

Answer: c

26. If the roots of the equations ax² + 2bx + c = 0 and bx² – 2√ac x + b = 0 are simultaneously real, then

(a) b = ac

(b) b2 = ac

(c) a2 = be

(d) c2 = ab

Answer: b

27. The roots of the equation (b – c) x² + (c – a) x + (a – b) = 0 are equal, then

(a) 2a = b + c

(b) 2c = a + b

(c) b = a + c

(d) 2b = a + c

Answer: d

28. A chess board contains 64 equal squares and the area of each square is 6.25 cm². A border round the board is 2 cm wide. The length of the side of the chess board is

(a) 8 cm

(b) 12 cm

(c) 24 cm

(d) 36 cm

Answer: c

29. One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Their present ages are

(a) 7 years, 49 years

(b) 5 years, 25 years

(c) 1 years, 50 years

(d) 6 years, 49 years

Answer: a

30. The sum of the squares of two consecutive natural numbers is 313. The numbers are

(a) 12, 13

(b) 13,14

(c) 11,12

(d) 14,15

Answer: a