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.

A Brief Description About Polynomials Class 10 MCQ And Answers PDF

Topic Name: | Polynomials Class 10 MCQ |

No of Questions: | 100 |

Questions Type: | Multiple Choice Questions |

Questions Format: | Text and PDF |

PDF Size: | 1 MB |

Download PDF: | Attached Below |

## Polynomials Class 10 MCQ and Answers

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

a) (6, 0)

b) (0, 7)

c) (0, 5)

d) (8, 9)

**Answer:** c

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

**Answer:** b

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

(a) 0

(b) 1

(c) 2

(d) 3

**Answer:** b

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

**Answer:** d

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

**Answer:** a

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

**Answer:** c

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

**Answer:** c

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

(a) 0

(b) 1

(c) 2

(d) 3

**Answer:** b

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

(a) 0

(b) 1

(c) 2

(d) 3

**Answer:** c

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

(a) 0

(b) 1

(c) 2

(d) 3

**Answer:** d

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

**Answer:** c

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

**Answer:** d

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

**Answer:** b

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

a) 3

b) 1

c) 2

d) 0

**Answer:** d

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

a) Linear

b) Quadratic

c) Cubic

d) Biquadratic

**Answer:** c

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

**Answer:** c

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

a) p(α)=4

b) p(α)=1

c) p(α)≠0

d) p(α)=0

**Answer:** d

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)

**Answer:** d

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

**Answer:** d

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

**Answer:** b

21. The value of a and b, if the zeros of x^{2}+(a+5)x-(b-4) are -5 and 9 will be _________

a) 47, -5

b) -5, 47

c) -9, 49

d) -4, 45

**Answer:** c

22. What will be the value of k, if one zero of x^{2}+(k-3)x-16=0 is additive inverse of other?

a) 4

b) -4

c) -3

d) 3

**Answer:** d

23. If α and β are the zeros of x^{2}+35x-75, then _______

a) α+β<αβ

b) α+β>αβ

c) α+β=αβ

d) α+β≠αβ

**Answer:** b

24. If α, β and γ are the zeros of 5x^{3} + 10×2 – x + 20, then the value of αβγ is _______

a) -1

b) 5

c) -10

d) -4

**Answer:** d

25. If α, β and γ are the zeros of 2x^{3} – 6x^{2} + 5x + 2, then the value of α + β + γ is _______

a) 0

b) 1

c) 3

d) 2

**Answer:** c

26. If α and β are the zeros of x^{2} + (k^{2} – 1)x – 20, such that α^{2} – β^{2} – αβ = 29 and α – β = 9 then, the value of k is _______

a) 1

b) 0

c) 2

d) 3

**Answer:** b

27. If α and β are the zeros of x^{2} + bx + c, then the polynomial having -α, -β as zeros is _______

a) -x^{2} – bx + c

b) x^{2} + bx + c

c) x^{2 }– bx + c

d) x^{2} – bx – c

**Answer:** c

28. If the two zeros of the polynomial x^{3} – 9x^{2} -x + 9, are 1 and 9, then the third zero is ________

a) 9

b) 1

c) 2

d) -1

**Answer:** d

29. What will be the value of a and b if the polynomial f(x)=30x^{4}-50x^{3}+109x^{2}-23x+25, when divided by 3x^{2}-5x+10, gives 10x^{2}+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

**Answer:** d

30. The quotient if the polynomial f(x)=50x^{2}-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

**Answer:** a

31. When a polynomial f(x)=acx^{3}+bcx+d, is divided by g(x), it leaves quotient as cx, and remainder as d. The value of g(x)will be _____

a) -ax^{2}+b

b) ax^{2}-b

c) ax^{2}+b

d) x^{2}+b

**Answer:** c

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 5x^{4}+10x^{3}-15x^{2}-5x is ____________

a) -12

b) -11

c) 11

d) 12

**Answer:** b

33. What real number that should be added to the polynomial f(x)=81x^{2}-31, so that it is exactly divisible by 9x+1?

a) 40

b) 10

c) 30

d) 20

**Answer:** c

34. If the polynomial f(x)=x^{2}+kx-15, is exactly divisible by x-5, then the value of k is _______

a) 3

b) 2

c) -3

d) -2

**Answer:** d

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

**Answer:** b

36. If the zeroes of the quadratic polynomial x^{2} + (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

**Answer:** d

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

(a) 1

(b) 2

(c) 3

(d) more than 3

**Answer:** d

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

**Answer:** a

39. The zeroes of the quadratic polynomial x^{2} + 99x + 127 are

(a) both positive

(b) both negative

(c) one positive and one negative

(d) both equal

**Answer:** b

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

**Answer:** a

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

**Answer:** c

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.

**Answer:** a

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

(a) 2

(b) 3

(c) 4

(d) more than 4

**Answer:** d

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

**Answer:** b

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

**Answer:** a

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

**Answer:** c

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

**Answer:** b

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

**Answer:** d

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

**Answer:** b