## 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
(c) cubic 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 x2 + 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
(c) cubic equation

8. 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
► (d) x2 – 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

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
► (d) ±2√6

11. Which of the following are the roots of the quadratic equation, x2 - 9x + 20 = 0 by factorisation?
(a) 3,4
(b) 4, 5
(c) 5, 6
(d) 6, 7
► (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

15. Value(s) of k for which the quadratic equation 2x2 -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 b2 - 4ac  for equation 3x2 - 7x - 2 = 0 is
(a) 49
(b) 0
(c) 25
(d) 73
► (d) 73

18. 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
► (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) 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
► (d) 2b = a + c

21. 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
► (c) p = 7

22. The equation x2 – px + q = 0 p, q ε R has no real roots if :
(a) p2 > 4q
(b) p2 < 4q
(c) p2 = 4q
(d) None of these
► (b) p2 < 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 ax2 + 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
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