# 100+ Polynomials Class 10 MCQ and Answers PDF

These 100+ Polynomials Class 10 MCQ and Answers PDF are most important for your upcoming class 10 examination. Polynomials Class 10 MCQ and Answers are based on NCERT class 10 maths chapter 2, composed by our special team. You can crack this exam easily with these PDF files.

## Polynomials Class 10 MCQ and Answers

1. The graph of the polynomial 2x2-8x+5 cuts the y-axis at __________

a) (6, 0)

b) (0, 7)

c) (0, 5)

d) (8, 9)

2. If the zeroes of the quadratic polynomial Ax² + Bx + C, C # 0 are equal, then

(a) A and B have the same sign

(b) A and C have the same sign

(c) B and C have the same sign

(d) A and C have opposite signs

3. If x3 + 1 is divided by x² + 5, then the possible degree of the quotient is

(a) 0

(b) 1

(c) 2

(d) 3

4. If x3 + 11 is divided by x² – 3, then the possible degree of remainder is

(a) 0

(b) 1

(c) 2

(d) less than 2

5. If x4 + 3x² + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are:

(a) 3, 0

(b) 4, 1

(c) 3, 1

(d) 4, 0

6. If x5 + 2×4 + x + 6 is divided by g(x), and quotient is x² + 5x + 7, then the possible degree of g(x) is:

(a) 4

(b) 2

(c) 3

(d) 5

7. If x5 + 2×4 + x + 6 is divided by g(x) and quo-tient is x² + 5x + 7, then the possible degree of remainder is:

(a) less than 1

(b) less than 2

(c) less than 3

(d) less than 4

8. What is the number of zeroes that a linear poly-nomial has/have:

(a) 0

(b) 1

(c) 2

(d) 3

9. What is the number(s) of zeroes that a quadratic polynomial has/have:

(a) 0

(b) 1

(c) 2

(d) 3

10. What is the number(s) of zeores that a cubic polynomial has/have:

(a) 0

(b) 1

(c) 2

(d) 3

11. If one of the zeroes of the cubic polynomial x3 + px² + qx + r is -1, then the product of the other two zeroes is

(a) p + q + 1

(b) p-q- 1

(c) q – p + 1

(d) q – p – 1

12. If one zero of the quadratic polynomial x² + 3x + b is 2, then the value of b is

(a) 10

(b) -8

(c) 9

(d) -10

13. If 1 is one of the zeroes of the polynomial x² + x + k, then the value of k is:

(a) 2

(b) -2

(c) 4

(d) -4

14. How many points will the graph of x2+2x+1 will cut the x-axis?

a) 3

b) 1

c) 2

d) 0

15. If the graph of a polynomial cuts the x-axis at 3 points, then the polynomial is ______

a) Linear

c) Cubic

16. What will be the nature of the zeros of a quadratic polynomial if it cuts the x-axis at two different points?

a) Real

b) Distinct

c) Real, Distinct

d) Complex

17. A real number is called zeros of the polynomial p(x) if _________

a) p(?)=4

b) p(?)=1

c) p(?)?0

d) p(?)=0

18. If the zeros of a polynomial are 3 and -5, then they cut the x-axis at ____ and _____ points.

a) (8, 0) and (-4, 0)

b) (3, -3) and (-5, 5)

c) (-3, 0) and (5, 0)

d) (3, 0) and (-5, 0)

19. If the graph of the quadratic polynomial is completely above or below the x-axis, then the nature of roots of the polynomial is _____

a) Real and Distinct

b) Distinct

c) Real

d) Complex

20. What will be the value of other zero, if one zero of the quadratic polynomial is 5 and the sum of the zeros is 10?

a) 10

b) 5

c) -5

d) -10

21. The value of a and b, if the zeros of x2+(a+5)x-(b-4) are -5 and 9 will be _________

a) 47, -5

b) -5, 47

c) -9, 49

d) -4, 45

22. What will be the value of k, if one zero of x2+(k-3)x-16=0 is additive inverse of other?

a) 4

b) -4

c) -3

d) 3

23. If ? and ? are the zeros of x2+35x-75, then _______

a) ?+?<??

b) ?+?>??

c) ?+?=??

d) ?+????

24. If ?, ? and ? are the zeros of 5x3 + 10×2 – x + 20, then the value of ??? is _______

a) -1

b) 5

c) -10

d) -4

25. If ?, ? and ? are the zeros of 2x3 – 6x2 + 5x + 2, then the value of ? + ? + ? is _______

a) 0

b) 1

c) 3

d) 2

26. If ? and ? are the zeros of x2 + (k2 – 1)x – 20, such that ?2 – ?2 – ?? = 29 and ? – ? = 9 then, the value of k is _______

a) 1

b) 0

c) 2

d) 3

27. If ? and ? are the zeros of x2 + bx + c, then the polynomial having -?, -? as zeros is _______

a) -x2 – bx + c

b) x2 + bx + c

c) x2 – bx + c

d) x2 – bx – c

28. If the two zeros of the polynomial x3 – 9x2 -x + 9, are 1 and 9, then the third zero is ________

a) 9

b) 1

c) 2

d) -1

29. What will be the value of a and b if the polynomial f(x)=30x4-50x3+109x2-23x+25, when divided by 3x2-5x+10, gives 10x2+3 as quotient and ax+b as remainder?

a) a=8, b=5

b) a=-8, b=5

c) a=8, b=-5

d) a=-8, b=-5

30. The quotient if the polynomial f(x)=50x2-90x-25 leaves a remainder of -5, when divided by 5x-10, will be __________

a) 10x+2

b) 10x-2

c) -10x+2

d) -10x-2

31. When a polynomial f(x)=acx3+bcx+d, is divided by g(x), it leaves quotient as cx, and remainder as d. The value of g(x)will be _____

a) -ax2+b

b) ax2-b

c) ax2+b

d) x2+b

32. The real number that should be subtracted from the polynomial f(x)=15×5+70×4+35×3-135×2-40x-11 so that it is exactly divisible by 5x4+10x3-15x2-5x is ____________

a) -12

b) -11

c) 11

d) 12

33. What real number that should be added to the polynomial f(x)=81x2-31, so that it is exactly divisible by 9x+1?

a) 40

b) 10

c) 30

d) 20

34. If the polynomial f(x)=x2+kx-15, is exactly divisible by x-5, then the value of k is _______

a) 3

b) 2

c) -3

d) -2

35. If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is

(a) 10

(b) -10

(c) 5

(d) -5

36. If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and -3, then

(a) a = -7, b = -1

(b) a = 5, b = -1

(c) a = 2, b = -6

(d) a – 0, b = -6

37. The number of polynomials having zeroes as -2 and 5 is

(a) 1

(b) 2

(c) 3

(d) more than 3

38. If one of the zeroes of the cubic polynomial x3 + ax² + bx + c is -1, then the product of the other two zeroes is

(a) b – a + 1

(b) b – a – 1

(c) a – b + 1

(d) a – b – 1

39. The zeroes of the quadratic polynomial x2 + 99x + 127 are

(a) both positive

(b) both negative

(c) one positive and one negative

(d) both equal

40. The zeroes of the quadratic polynomial x² + kx + k, k? 0,

(a) cannot both be positive

(b) cannot both be negative

(c) are always unequal

(d) are always equal

41. If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then

(a) c and a have opposite signs

(b) c and b have opposite signs

(c) c and a have the same sign

(d) c and b have the same sign

42. If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it

(a) has no linear term and the constant term is negative.

(b) has no linear term and the constant term is positive.

(c) can have a linear term but the constant term is negative.

(d) can have a linear term but the constant term is positive.

43. The number of polynomials having zeroes as 4 and 7 is

(a) 2

(b) 3

(c) 4

(d) more than 4

44. A quadratic polynomial, whose zeores are -4 and -5, is

(a) x²-9x + 20

(b) x² + 9x + 20

(c) x²-9x- 20

(d) x² + 9x- 20

45. The zeroes of the quadratic polynomial x² + 1750x + 175000 are

(a) both negative

(b) one positive and one negative

(c) both positive

(d) both equal

46. The zeroes of the quadratic polynomial x² – 15x + 50 are

(a) both negative

(b) one positive and one negative

(c) both positive

(d) both equal

47. The zeroes of the quadratic polynomial 3x² – 48 are

(a) both negative

(b) one positive and one negative

(c) both positive

(d) both equal

48. The zeroes of the quadratic polynomial x² – 18x + 81 are

(a) both negative

(b) one positive and one negative

(c) both positive and unequal

(d) both equal and positive

49. The zeroes of the quadratic polynomial x² + px + p, p ? 0 are

(a) both equal

(b) both cannot be positive

(c) both unequal

(d) both cannot be negative