Mathematics homework help. 1. Find the zeroes of the quadratic polynomial x

2

+7x + 12

(1) -2, -5

(2) -3, -4

(3) 2, 5

(4) 3, 4

Ans : (2)

2. Find the zeroes of the polynomial x2

– 17

(1)

(2)

(3)

(4) none of these

Ans : (1)

3. Find a quadratic polynomial, the sum and product of whose zeroes are -7 and -2

(1) x2

-7x -2

(2) x

2

-7 x + 2

(3) x

2

+ 7x -2

(4) x

2

+ 2x -7

Ans : (3)

4. Find a cubic polynomial when the zeroes are 3, -1,

(1) 3×3

– 5×2

– 11x -3

(2) 3×3

+ 5×2 + 11x -3

(3) 3×3

-5×2

+ 11x + 3

(4) none of these

Ans : (1)

5. Find a quadratic polynomial, the sum and product of whose zeroes are

(1) 4×2

– x + 1

(2) 4×2 + x – 1

(3) 4×2 + x + 1

(4) none of these

Ans : (3)

6. Find all the zeroes of 2×4

– 3×3

– 3×2 + 6x – 2 if two of its zeroes are and

(1)

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(2)

(3)

(4)

Ans : (4)

7. Find the quotient and remainder when the polynomial x

4

– 3×2 + 4x + 5 is divided by x

2

– x + 1

(1) x

2

+ x – 3, 8

(2) x

2

– x + 3, 7

(3) x2

– x -3, 4

(4) x

2 + 2x + 3, 6

Ans : (1)

8. The quotient and remainder are x – 2 and -2x + 4 respectively. If the polynomial x

3

– 3×2 + x + 2

is divided by g(x). Find g(x)

(1) x

2 + x + 1

(2) x2

– x – 1

(3) x

2

– x + 1

(4) none of these

Ans : (3)

9. Find P and q, if the zeroes of the polynomial x

3

– 3×2

+ x + 1 are p-q, p, p + q

(1)

(2)

(3)

(4)

Ans : (4)

10. Find a quadratic polynomial whose zeroes are and

(1) x

2

– 7x + 10

(2) x

2

+ 7x + 10

(3) x2

– 7x – 10

(4) x

2 + 7x – 10

Ans : (1)

11. If the quotient and remainder were 3y – 5 and 9y + 10, on dividing 3y3

+ y

2 + 2y + 5 by g (y).

Find g (y)

(1) y

2

– 2y + 1

(2) y2 + 2y + 1

(3) y

2

-2y – 1

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(4) 2y2

– 2y – 1

Ans : (2)

12. Obtain the zeroes of the quadratic polynomial pqx

2

+ (q2

– Pr) x – qr

(1)

(2)

(3)

(4)

Ans : (1)

13. If two of the zeroes are and . Find the other zeroes of t4

– 6t3

– 26t2 + 138t – 35

(1) 7 and 5

(2) 7 and – 5

(3) (-6, 7)

(4) (-5 and -7)

Ans : (2)

14. If p and q are the zeroes of the quadratic polynomial 4×2

– 1 = 0. Find the value of p2

+ q2

(1) 3/2

(2)

(3)

(4) 1

Ans : (3)

15. Find the zeroes of the quadratic polynomial x

2

+ 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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17. Find the zeroes of the polynomial x

2

– 21

(1)

(2) -3, 3

(3)

(4) none of these

Ans : (1)

18. Find the sum and product of the zeroes of polynomial x

2

– 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 19×2

– 16x – 21

(1)

(2)

(3)

(4)

Ans : (4)

20. If p and q are the zeroes of the polynomial x

2

– 5x – k. Such that p – q = 1, find the value of K

(1) 6

(2) 7

(3) 8

(4) 9

Ans : (1)

21. Find the sum and product of the zeroes of cubic polynomial 2×3

– 5×2

– 14x + 8.

(1) 5/2, 7, -4

(2) -5/2, 7, -4

(3) -5/2, -7, 4

(4) 5/2, -7, 4

Ans : (1)

22. Find the zeroes of the polynomial 4×2

– 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

(1) – x

2

+ 2, 5x – 10

(2) -x

2

– 2, – 5x + 10

(3) x

2

+ 2, 5x – 10

(4) x

2

-2, – 5x + 10

Ans : (2)

24. Form a quadratic polynomial of which one zero is and the sum of the zeroes is 12

(1) x

2

– 4x + 30

(2) x

2 + 4x – 31

(3) x

2

– 12x + 31

(4) none of these

Ans : (3)

25. Find the value of a so that -2 is a root of 2×2

– x + a = 0

(1) 10

(2) – 10

(3) 9

(4) -9

Ans : (2)

26. If p and q are the zeroes of the quadratic polynomial 2×3

+ 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)

28. If P and q are the zeroes of the quadratic polynomial x

2

+ mx + n

2

+ a, then the value of p

2

+

q

2

+ pq is

(1) 0

(2) a

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(3) -a

(4)

Ans : (3)

29. If , are the zeroes of the equation ax

2

+ bx + c = 0, them form the quadratic polynomial

whose zeroes are 2 + 3 , 3 + 2

(1)

(2) a

2

x

2

+ 5abx + 6b2

+ ac

(3) ax2

+ abx + 6b2

+ ac

(4) a2

x

2

+ abx + b2

+ ac

Ans : (1)

30. If p and q are the zeroes of the polynomial x

2

+ px + q = 0, then

(1) p = 1

(2) p = 1 or 0

(3) p = -2

(4) p = -2 or 0

Ans : (2)

31. If one zero of quadratic polynomial x

2

– 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)

33. If the product of zeroes of the quadratic polynomial mx2

+ 6x + (2m-1) is -1, then find the

value of m

(1)

(2) 3

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(3)

(4) – 3

Ans : (1)

34. If the zeroes of the quadratic polynomial ax2

+ bx +c are of the form and , then find

the value of (a + b + c)2

(1) b2

+ 4ac

(2) b2

– 4ac

(3) a

2

+ 4ac

(4) c2 + 4ab

Ans : (2)

35. If , are the zeroes of the quadratic polynomial ax2

+ bx +c , then form the quadratic

polynomial whose zeroes are and is

(1)

(2)

(3)

(4)

Ans : (1)

36. If the difference of the zeroes of the quadratic polynomial x

2

– bx + c be 1, then

(1)

(2)

(3)

(4)

Ans : (1)

37. If , are the zeroes of the quadratic polynomial ax2

+ bx + c, then is

(1) 2 / a

(2) 2 / b

(3) 2 / c

(4) – 2 / a

Ans : (4)

38. Find the zeroes of the polynomial x

2

+ 2x + 1 = 0

(1) – 1, -1

(2) 1, 1

(3) – 1, 1

(4) -2, 1

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Ans : (1)

39. Find the zeroes of the quadratic polynomial 6×2

– 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 quadratic polynomial 5×2

– 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)

42. Find the sum and product of zeroes of the cubic polynomial p (x) = 5×3

– 10×2

+ 7x + 15

(1) 2, 7/5, -3

(2) -2 , -7/5, 3

(3) 2, -7/5, 3

(4) -2, – 7/5, -3

Ans : (1)

43. Find the remainder when y

3

+ 4y2

– 3y + 10 is divided by y + 4

(1) 22

(2) -22

(3) 21

(4) 20

Ans : (1)

44. Find the quotient and remainder when 2t4

– 6t3 + 2t2

– t + 2 is divided by t + 2

(1) 2t3

+ 10t2

-22t + 45, 91

(2) 2t2

-20t + 45, 90

(3) 2t3

– 10t2

+ 22t – 45, 92

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(4) 2t3

-22t + 45, 91

Ans : (3)

45. Find the quotient and remainder when 4y3

-12y2 + 14y -13 is divided by t –

(1) 4t2

-10t + 9 , -17/2

(2) 4t2 + 10t -9 , 17/2

(3) 4t2

-10t – 9, 19/2

(4) 4t2

+ 4t + 5, 17/2

Ans : (1)

46. If p and q are the zeroes of x

2

– 5x + 4 = 0, find the value of p2

q + q2

p

(1) 19

(2) 16

(3) 17

(4) 20

Ans : (4)

47. Find the quotient and remainder when t4

+ 1 is divided by t – 1

(1) t3

– t2

– t – 1, 3

(2) t3

– t2 + t – 1, 4

(3) t3

+ t2 + t + 1, 2

(4) t3

– t2

– t + 1, 2

Ans : (3)

48. Find the quotient and remainder when y4

+ y2

+1 is t3

divided by y2 + y + 1

(1) y

2

– y + 1, 0

(2) y

2 + y + 1, 1

(3) y

2

– y – 1, 0

(4) y

2

+ y -1, 2

Ans : (1)

49. Form the quadratic polynomial in t when zeroes are and

(1) t2

– 2t – 1

(2) t2

– 4t – 1

(3) t2

+ t + 1

(4) t2

– t – 1

Ans : (2)

50. If and are the zeroes of x

2

– 6x + 4 = 0, Find the value of 2 2

+ 2 3

(1) 92

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(2) 94

(3) 96

(4) 90