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MCQs for Class 10 Maths Chapter 2 Polynomials

Maths Chapter 2
Polynomials

MCQ

1. 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) -10

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

(a) 1

(b) 2

(c) 3

(d) more than 3

Answer: (d) more than 3

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

(a)c and b have opposite signs

(b)c and a have opposite signs

(c)c and b have same signs

(d)c and a have same signs

Answer: (d) c and a have same signs

4. A polynomial of degree 3 is called

(a) a linear polynomial

(b) a quadratic polynomial

(c) a cubic polynomial

(d) a biquadratic polynomial

Answer: (c) a cubic polynomial

5. Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial

(a) intersects y-axis

(b) intersects x-axis

(c) intersects y-axis or intersects x-axis

(d) none of these

Answer: (c) intersects y-axis or intersects x-axis

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6. 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) both negative

7. 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) b – a + 1

8. 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) has no linear term and the constant term is negative.

9. If p(x) is a polynomial of degree one and p(a) = 0, then a is said to be: (a) Zero of p(x) (b) Value of p(x) (c) Constant of p(x) (d) None of the above

Answer: (a) Zero of p(x)

10. Dividend is equal to

(a) divisor × quotient + remainder

(b) divisior × quotient

(c) divisior × quotient – remainder

(d) divisor × quotient × remainder

Answer: (a) divisor × quotient + remainder

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11. What should be subtracted from x³ – 2x² + 4x + 1 to get 1?

(a) x³ – 2x² + 4x

(b) x³ – 2x² + 4 + 1

(c) -1

(d) 1

Answer: (a) x³ – 2x² + 4x

12. 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

Answer: (b) both negative

13. 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) c and a have the same sign

14. A polynomial of degree n has: (a) Only one zero (b) At least n zeroes (c) More than n zeroes (d) Atmost n zeroes

Answer: (d) Atmost n zeroes

15. Find the quadratic polynomial whose zeros are 2 and -6

(a) x2 + 4x + 12

(b) x2 – 4x – 12

(c) x2 + 4x – 12

(d) x2 – 4x + 12

Answer: (c) x2 + 4x – 12

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16. If a polynomial of degree 4 is divided by quadratic polynomial, the degree of the remainder is

(a) ≤ 1

(b) ≥ 1

(c) 2
(d) 4

Answer: (a) ≤ 1

17. If α, β are the zeroes of the polynomial x² – 16, then αβ(α + β) is

(a) 0

(b) 4

(c) -4

(d) 16

Answer: (a) 0

18. What is the quadratic polynomial whose sum and the product of zeroes is √2, ⅓ respectively?

(a) 3×2-3√2x+1

(b) 3×2+3√2x+1

(c) 3×2+3√2x-1

(d) None of the above

Answer: (a) 3×2-3√2x+1

19. If α, β, γ are the zeroes of the cubic polynomial ax³ + bx² + cx + d then αβ + βγ + αγ is equal to

(a) −b/a

(b) b/a

(c) c/a

(d) d/a
Answer: (c) c/a

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20. Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is

(a) –c/a

(b) c/a

(c) 0

(d) 3

Answer: (b) c/a

21. Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial is:

(a) Intersects x-axis

(b) Intersects y-axis

(c) Intersects y-axis or x-axis

(d) None of the above

Answer: (a) Intersects x-axis

22. If the point (5,0), (0-2) and (3,6) lie on the graph of a polynomial. Then which of the following is a zero of the polynomial?

(a) 5

(b) 6

(c) not defined

(d) -2

Answer: (a) 5

23. If α and 1/α are the zeroes of the polynomial ax² + bx + c, then value of c is

(a) 0

(b) a

(c) -a

(d) 1

Answer: (b) a

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24. The zeroes of x2–2x –8 are:

(a) (2,-4)

(b) (4,-2)

(c) (-2,-2)

(d) (-4,-4)

Answer: (b) (4,-2)

25. Every linear polynomial has — zero.

(a) Only one

(b) Two

(c) Three

(d) Four

Answer: (a) Only one

26. Zeroes of p(x) = x2-27 are:

(a) ±9√3

(b) ±3√3

(c) ±7√3

(d) None of the above

Answer: (b) ±3√3

27. If the zeroes of the polynomial x³ – 3x² + x – 1 are st, s and st then value of s is

(a) 1

(b) -1

(c) 2

(d) -3

Answer: (a) 1

28. Graph of a quadratic polynomial is a ———

(a) Straight line

(b) Parabola

(c) Circle

(d) Hyperbola

Answer: (b) Parabola

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29.If sum of the squares of zeroes of the quadratic polynomial 6×2 + x + k is 25/36, the value of k is:

(a) 4

(b) – 4
(c) 2

(d) – 2

Answer: (d) -2

30. If p(x) is a polynomial of degree one and p(a) = 0, then a is said to be: (a) Zero of p(x) (b) Value of p(x) (c) Constant of p(x) (d) None of the above

Answer: (a) Zero of p(x)

31. The number of zeros of a cubic polynomial is

(a) 3

(b) at least 3

(c) 2

(d) at most 3

Answer: (d) at most 3

32. A polynomial p (x) of degree n has at most ——– zeroes.

(a) 1

(b) n

(c) n + 1
(d) n + 2

Answer: (b) n

33. The sum and the product of the zeroes of polynomial 6x² – 5 respectively are

(a) 0, −65

(b) 0, 65

(c) 0, 56

(d) 0, −56

Answer: (d) 0, −56

34. Sum and the product of zeroes of the polynomial x2 +7x +10 is

(a) 10/7 and -10/7

(b) 7/10 and -7/10

(c) -7 and 10

(d) 7 and -10

Answer: (c) -7 and 10

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35. 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) 1

36. The graph of the polynomial f(x) = 2x – 5 intersects the x – axis at

(a) (5/2, 0)

(b) (-5/2, 0)

(c) (-5/2, 5/2)

(d) (5/2, -5/2)

Answer: (a) (5/2, 0)

37. The value of p for which the polynomial x3 + 4×2 –px + 8 is exactly divisible by (x – 2) is:

(a) 0

(b) 3

(c) 5

(d) 16

Answer: (d) 16

38. A polynomial of degree n has:

(a) Only one zero

(b) At least n zeroes

(c) More than n zeroes

(d) Atmost n zeroes

Answer: (d) Atmost n zeroes

39. The zero of the linear polynomial ax + b is

(a) –a/b

(b) –b/a

(c) 0

(d) none

Answer: (b) –b/a

40. 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) -10

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