## MCQ Questions for Class 10 Maths: Ch 4 Quadratic Questions

1. 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

► (a) linear equation

2. The quadratic equation 2x2 – 3x + 5 = 0 has

(a) Real and distinct roots

(b) Real and equal roots

(c) Imaginary roots

(d) All of the above

► (c) Imaginary roots

3. The quadratic equation has degree

(a) 0

(b) 1

(c) 2

(d) 3

► (c) 2

4. If 7th and 13th term of an A.P. are 34 and 64 respectively, then its 18th term is

(a) 87

(b) 88

(c) 89

(d) 90

► (c) 89

5. Two candidates attempt to solve a quadratic equation of the form x

^{2}+ px + q = 0. One starts with a wrong value of p and finds the roots to be 2 and 6. The other starts with a wrong value of q and finds the roots to be 2 and – 9. Find the correct roots of the equation :
(a) 3, 4

(b) - 3, - 4

(c) 3, – 4

(d) – 3, 4

► (b) - 3, - 4

6. A bi-quadratic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

► (d) 4

7. The equation (x – 2)

^{2}+ 1 = 2x – 3 is a

(a) linear equation

(b) quadratic equation

(c) cubic equation

(d) bi-quadratic equation

► (b) quadratic equation

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

(a) x

^{2}– 7x + 5 = 0
(b) x

^{2}+ 7x + 6 = 0
(c) x

^{2}– 7x + 6 = 0
(d) x

► (d) x

^{2}– 6x + 7 = 0► (d) x

^{2}– 6x + 7 = 0
9. Reduction of a rupee in the price of onion makes the possibility of buying one more kg of onion for Rs.56. Find the original price of the onion per kg?

(a) 7

(b) 1

(c) 7, -8

(d) 8

► (d) 8

(a) 7

(b) 1

(c) 7, -8

(d) 8

► (d) 8

10. The equation 2x

^{2}+ kx + 3 = 0 has two equal roots, then the value of k is
(a) ±√6

(b) ± 4

(c) ±3√2

(d) ±2√6

► (d) ±2√6

► (d) ±2√6

11. Which of the following are the roots of the quadratic equation, x

^{2}- 9x + 20 = 0 by factorisation?
(a) 3,4

(b) 4, 5

(c) 5, 6

(d) 6, 7

► (b) 4, 5

► (b) 4, 5

12. The cubic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

► (c) 3

13. Find the two consecutive odd positive integers, sum of whose square is 290

(a) 15, 17

(b) 9, 11

(c) 13, 15

(d) 11, 13

► (d) 11, 13

14. The sum of the roots of the quadratic equation 3×

^{2}– 9x + 5 = 0 is
(a) 3

(b) 6

(c) -3

(d) 2

► (c) -3

► (c) -3

15. Value(s) of k for which the quadratic equation 2x

^{2}-kx + k = 0 has equal roots is
(a) 0

(b) 4

(c) 8

(d) 0 and 8

► (d) 0 and 8

16. 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

► (a) a, b

17. The value of b

^{2}- 4ac for equation 3x^{2}- 7x - 2 = 0 is
(a) 49

(b) 0

(c) 25

(d) 73

► (d) 73

18. If the roots of px

^{2}+ qx + 2 = 0 are reciprocal of each other, then
(a) P = 0

(b) p = -2

(c) p = ±2

(d) p = 2

► (d) p = 2

► (d) p = 2

19. The two consecutive odd positive integers, sum of whose squares is 290 are

(a) 13, 15

(b) 11, 13

(c) 7, 9

(d) 5, 7

► (b) 11, 13

20. The roots of the equation (b – c) x

^{2}+ (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

► (d) 2b = a + c

21. If -5 is a root of the quadratic equation 2x

(a) p = 3

(b) p = 5

(c) p = 7

(d) p = 1

► (c) p = 7

^{2}+ px – 15 = 0, then(a) p = 3

(b) p = 5

(c) p = 7

(d) p = 1

► (c) p = 7

22. The equation x

(a) p

(b) p

(c) p

(d) None of these

► (b) p

^{2}– px + q = 0 p, q Îµ R has no real roots if :(a) p

^{2}> 4q(b) p

^{2}< 4q(c) p

^{2}= 4q(d) None of these

► (b) p

^{2}< 4q
23. 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

► (a) 7 years, 49 years

24. If (x – a) is one of the factors of the polynomial ax

^{2}+ bx + c, then one of the roots of ax² + bx + c = 0 is
(a) 1

(b) c

(c) a

(d) none of these

► (c) a