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Class - X Polynomials 2
1. Find the zeroes of the quadratic quadra tic polynomial polynomial x +7x + 12 (1) -2, -5 (2) -3, -4 (3) 2, 5 (4) 3, 4 Ans : (2) 2. Find the zeroes of the polynomial polynomial x 2 - 17 (1) (2) (3) (4) none of these Ans : (1) 3. Find a quadratic polynomial, polynomial, the sum and product of whose zeroes are -7 and -2 (1) x2 -7x -2 2
(2) x -7 x + 2 (3) x2 + 7x -2 2
(4) x + 2x -7 Ans : (3) 4. Find a cubic polynomial polynomial when the zeroes are 3, -1, 3
2
(1) 3x - 5x - 11x -3 (2) 3x3 + 5x2 + 11x -3 (3) 3x3 -5x2 + 11x + 3 (4) none of these Ans : (1) 5. Find a quadratic polynomial, polynomial, the sum and product of whose zeroes are (1) 4x2 - x + 1 2
(2) 4x + x - 1 2
(3) 4x + x + 1 (4) none of these Ans : (3) 6. Find all the zeroes of 2x 4 - 3x3 - 3x2 + 6x - 2 if two of its zeroes are (1)
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and
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(2) (3) (4) Ans : (4) 7. Find the quotient and remainder when the polynomial x4 - 3x2 + 4x + 5 is divided by x 2 - x + 1 2
(1) x + x - 3, 8 2
(2) x - x + 3, 7 (3) x2 - x -3, 4 2
(4) x + 2x + 3, 6 Ans : (1) 3
2
8. The quotient and remainder are x - 2 and -2x + 4 respectively. If the polynomial x - 3x + x + 2 is divided by g(x). Find g(x) 2
(1) x + x + 1 (2) x2 - x - 1 2
(3) x - x + 1 (4) none of these Ans : (3) 3
2
9. Find P and q, if the zeroes of the polynomial x - 3x + x + 1 are p-q, p, p + q (1) (2) (3) (4) Ans : (4) 10. Find a quadratic polynomial whose zeroes are
and
2
(1) x - 7x + 10 2
(2) x + 7x + 10 (3) x2 - 7x - 10 2
(4) x + 7x - 10 Ans : (1) 3
2
11. If the quotient and remainder were 3y - 5 and 9y + 10, on dividing 3y + y + 2y + 5 by g (y). Find g (y) 2
(1) y - 2y + 1 (2) y2 + 2y + 1 2
(3) y -2y - 1
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2
(4) 2y - 2y - 1 Ans : (2) 2
2
12. Obtain the zeroes of the quadratic polynomial pqx + (q - Pr) x - qr (1) (2) (3) (4) Ans : (1) 13. If two of the zeroes are (1) 7 and 5 (2) 7 and - 5 (3) (-6, 7) (4) (-5 and -7)
and
4
3
2
. Find the other zeroes of t - 6t - 26t + 138t - 35
Ans : (2) 2
2
14. If p and q are the zeroes of the quadratic polynomial 4x - 1 = 0. Find the value of p + q (1) 3/2 (2) (3) (4) 1 Ans : (3) 15. Find the zeroes of the quadrat ic polynomial x2 + 19 x + 90 (1) -9, -10 (2) 9, 10 (3) 4, 5 (4) -4, -5 Ans : (1) 16. Find the sum and product of zeroes of the polynomial (1) (2) (3) (4) Ans : (2)
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2
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2
17. Find the zeroes of the polynomial x - 21 (1) (2) -3, 3 (3) (4) none of these Ans : (1) 2
18. Find the sum and product of the zeroes of polynomial x - 51 (1) 0, 51 (2) 0, -51 (3) 2, 51 (4) -2, 51 Ans : (2) 19. Find the sum and product of the zeroes of quadratic polynomial 19x 2 - 16x - 21 (1) (2) (3) (4) Ans : (4) 2
20. If p and q are the zeroes of the polynomial x - 5x - k. Such that p - q = 1, find the value of K (1) 6 (2) 7 (3) 8 (4) 9 Ans : (1) 3
2
21. Find the sum and product of the zeroes of cubic polynomial 2x - 5x - 14x + 8. (1) 5/2, 7, -4 (2) -5/2, 7, -4 (3) -5/2, -7, 4 (4) 5/2, -7, 4 Ans : (1) 2
22. Find the zeroes of the polynomial 4x - 4x + 1 (1) (2) (3) 1 (4)
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Ans : (2) 23. Find the quotient and remainder, when the polynomial x 4 - 5x + 6 is divided by 2 - x 2 2
(1) - x + 2, 5x - 10 2
(2) -x - 2, - 5x + 10 2
(3) x + 2, 5x - 10 2
(4) x -2, - 5x + 10 Ans : (2) 24. Form a quadratic polynomial of which one zero is
and the sum of the zeroes is 12
(1) x2 - 4x + 30 2
(2) x + 4x - 31 2
(3) x - 12x + 31 (4) none of these Ans : (3) 2
25. Find the value of a so that -2 is a root of 2x - x + a = 0 (1) 10 (2) - 10 (3) 9 (4) -9 Ans : (2) 3
26. If p and q are the zeroes of the quadratic polynomial 2x + 3x + 5. Find the value of (1) 3/5 (2) 5/3 (3) -3/5 (4) - 5/3 Ans : (3) 27. Find the quadratic polynomial whose sum and product of its zeroes are
and
respectively
(1) (2) (3) (4) none of these Ans : (1) 2
2
2
28. If P and q are the zeroes of the quadratic polynomial x + mx + n + a, t hen the value of p + 2
q + pq is (1) 0 (2) a
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(3) -a (4) Ans : (3) 2
29. If , are the zeroes of the equation ax + bx + c = 0, them form the quadra tic polynomial whose zeroes are 2 + 3 , 3 + 2 (1) (2) a2 x2 + 5abx + 6b 2 + ac 2
2
2 2
2
(3) ax + abx + 6b + ac (4) a x + abx + b + ac Ans : (1) 2
30. If p and q are the zeroes of the polynomial x + px + q = 0, then (1) p = 1 (2) p = 1 or 0 (3) p = -2 (4) p = -2 or 0 Ans : (2) 2
31. If one zero of quadratic polynomial x - x - k is the square of other, then find k (1) (2) (3) (4) Ans : (3) 32. If
and
are the zeroes of quadratic polynomial ax2 + bx + c = 0, then find the value of
(1) (2) (3) (4) Ans : (1) 2
33. If the product of zeroes of the quadratic polynomial mx + 6x + (2m-1) is -1, then find the value of m (1) (2) 3
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(3) (4) - 3 Ans : (1) 2
34. If the zeroes of the quadratic polynomial ax + bx +c are of the form the value of (a + b + c)
and
, then find
2
2
(1) b + 4ac (2) b2 - 4ac 2
(3) a + 4ac 2
(4) c + 4ab Ans : (2) 35. If
,
2
are the zeroes of the quadratic polynomial ax + bx +c , then form the quadratic
polynomial whose zeroes are
and
is
(1) (2) (3) (4) Ans : (1) 2
36. If the difference of the zeroes of the quadratic polynomial x - bx + c be 1, then (1) (2) (3) (4) Ans : (1) 37. If
,
2
are the zeroes of the quadratic polynomial ax + bx + c, then
(1) 2 / a (2) 2 / b (3) 2 / c (4) - 2 / a Ans : (4) 2
38. Find the zeroes of the polynomial x + 2x + 1 = 0 (1) - 1, -1 (2) 1, 1 (3) - 1, 1 (4) -2, 1
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is
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Ans : (1) 39. Find the zeroes of the quadrat ic polynomial 6x2 - 7x - 3 (1) 3/2 (2) - 3/2 , 1/3 (3)
, - 1/3
(4) 3/2 , - 1/3 Ans : (4) 40. Find the zeroes of the quadrat ic polynomial 5x2 - 4 - 8x (1) 2/5, -2 (2)
, -2
(3) 2, -2/5 (4) 2/5, 2 Ans : (3) 41. Find the quadratic polynomial whose zeroes are
and
respectively
(1) (2) (3) (4) None of these Ans : (2) 3
2
42. Find the sum and product of zeroes of the cubic polynomial p (x) = 5x - 10x + 7x + 15 (1) 2, 7/5, -3 (2) -2 , -7/5, 3 (3) 2, -7/5, 3 (4) -2, - 7/5, -3 Ans : (1) 3
2
43. Find the remainder when y + 4y - 3y + 10 is divided by y + 4 (1) 22 (2) -22 (3) 21 (4) 20 Ans : (1) 4
3
2
44. Find the quotient and remainder when 2t - 6t + 2t - t + 2 is divided by t + 2 3
2
(1) 2t + 10t -22t + 45, 91 (2) 2t2 -20t + 45, 90 3
2
(3) 2t - 10t + 22t - 45, 92
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3
(4) 2t -22t + 45, 91 Ans : (3) 3
2
45. Find the quotient and remainder when 4y -12y + 14y -13 is divided by t 2
(1) 4t -10t + 9 , -17/2 (2) 4t2 + 10t -9 , 17/2 2
(3) 4t -10t - 9, 19/2 2
(4) 4t + 4t + 5, 17/2 Ans : (1) 2
2
2
46. If p and q are the zeroes of x - 5x + 4 = 0, find the value of p q + q p (1) 19 (2) 16 (3) 17 (4) 20 Ans : (4) 4
47. Find the quotient and remainder when t + 1 is divided by t - 1 3
2
3
2
(1) t - t - t - 1, 3 (2) t - t + t - 1, 4 (3) t3 + t 2 + t + 1, 2 (4) t3 - t2 - t + 1, 2 Ans : (3) 48. Find the quotient and remainder when y 4 + y2 +1 is t3 divided by y2 + y + 1 (1) y2 - y + 1, 0 2
(2) y + y + 1, 1 2
(3) y - y - 1, 0 2
(4) y + y -1, 2 Ans : (1) 49. Form the quadratic polynomial in t when zeroes are
and
2
(1) t - 2t - 1 2
(2) t - 4t - 1 2
(3) t + t + 1 (4) t2 - t - 1 Ans : (2) 50. If (1) 92
and
2
are the zeroes of x - 6x + 4 = 0, Find the value of
2 2
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+
2 3
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(2) 94 (3) 96 (4) 90 Ans : (3)
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