CBSE Class 10 Mathematics Polynomials MCQs

Question :  If 5 is a zero of the quadratic polynomial x² - kx -15, then the value of k is

a) 2

b) –2

c) 4

d) – 4

Answer : 2

Question : A quadratic polynomial with 3 and 2 as the sum and product of its zeroes respectively is

a) x² -3x +2

b) x² -2x +2

c) x² -2x -2

d) None of these

Answer :  x² -3x +2

Question : A quadratic polynomial, whose zeroes are 5 and –8 is

a) x² +3x - 40

b) None of these

c) x² -3x - 40

d) x² -13x - 40

Answer :  x² +3x - 40

Question : The number of polynomials having exactly two zeroes 1 and –2 is

a) 1

b) 2

c) 3

d) infinitely many

Answer : 1

Question :  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) 0

c) -b/a

d) -c/a

Answer : c/a

Question :  Given that two of the zeroes of the cubic polynomial ax 3 + bx² + cx + d are 0, the value of c is

a) equal to 0

b) can’t say

c) greater than 0

d) less than 0

Answer : equal to 0

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

a) c and a have the same sign

b) c and b have the same sign

c) c and a have opposite signs

d) c and b have opposite signs

Answer : c and a have the same sign

Question :  The zeroes of the quadratic polynomial x² + kx + k, k ¹ 0

a) cannot both be positive

b) are always equal

c) cannot both be negative

d) are always unequal

Answer : cannot both be positive

Question :  The zeroes of the quadratic polynomial x² + ax + b a, b > 0 are

a) both negative

b) both positive

c) one positive one negative

d) can’t say

Answer : both negative

Question : If the graph of a polynomial intersects the x-axis at exactly two points, then it

a) can be a cubic or a quadratic polynomial

b) cannot be a linear or a cubic polynomial

c) can be a quadratic polynomial only

d) can be a linear or a quadratic polynomial

Answer : can be a cubic or a quadratic polynomial

Question :  The zeroes of the quadratic polynomial x² +99x +127 are

a) both negative

b) both equal

c) both positive

d) one positive and one negative

Answer : both negative

Question : Which of the following is not the graph of a quadratic polynomial?

a)

b)

c)

d)

Answer :

Question :

a) –1, –1

b) 1, –1

c) 1, 1

d) 3, –3

Answer : –1, –1

Question : Which of the following is a polynomial

a) 3x² -3x +1

b) x² + x^-2 +7

c) 2x² -3x +1

d) None of these

Answer :  3x² -3x +1

Question :  If one zero of the quadratic polynomial x² -5x + k is –4 ,then the value of k is

a) –36

b) 18

c) –18

d) 36

Answer : –36

Question :  If the zeroes of the quadratic polynomial x² +(a +1)x + b are 2 and –3, then

a) a = 0, b = -6

b) a = 2, b = -6

c) a = 5, b = -1

d) a = -7, b = -1

Answer : a = 0, b = -6

Question : If a polynomial of degree 6 is divided by a polynomial of degree 2, then the degree of the

a) equal to 4

b) equal to 2

c) less than 2

d) less than 4

Answer : equal to 4

Question :  If one of the zeroes of a quadratic polynomial of the form x² + ax + b is 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 positive

d) can have a linear term but the constant term is negative

Answer : has no linear term and the constant term is negative

Question : A quadratic polynomial with sum and product of its zeroes as 8 and –9 respectively is

a) x² -8x -9

b) x² + 8x -9

c) x² - 8x +9

d) None of these

Answer :  x² -8x -9

Question :  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) a - b -1

b) b - a -1

c) b - a +1

d) a - b +1

Answer : a - b -1

Question : The quadratic polynomial having zeroes –3 and 2 is

a) x² + x -6

b) x² + x +6

c) x² - x +6

d) x² - x -6

Answer :  x² + x -6

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

a) c and a have the same sign

b) c and a have opposite signs

c) c and b have opposite signs

d) c and b have the same sign

Answer : c and a have the same sign

Question :  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 : has no linear term and the constant term is negative.

Question :  If the zeroes of the quadratic polynomial x² +(a +1) x + b are 2 and –3, then

a) a = 0, b = -6

b) a = 2, b = -6

c) a = 5, b = -1

d) a = -7, b = -1

Answer : a = 0, b = -6

Question :  If f(x) = ax² + bx + c has no real zeroes and a + b + c < 0, then

a) c > 0

b) c < 0

c) none of these

d) c = 0

Answer : c > 0

Question. If α,β are the zeroes of the polynomials f(x) = x² + x + 1, then 1/α + 1/β
(a) 0
(b) 1
(c) –1
(d) none of these

Question. If one of the zero of the polynomial f(x) = (k² + 4)x² + 13x + 4k is reciprocal of the other then k =
(a) 2
(b) 1
(c) –1
(d) – 2

Question. If α,β are the zeroes of the polynomials f(x) = 4x² + 3x + 7, then 1/α + 1/β 
(a) 7/3
(b) -7/3
(c) 3/7
(d) -3/7

Question. If the sum of the zeroes of the polynomial f(x) = 2x³ – 3kx² + 4x – 5 is 6, then value of k is
(a) 2
(b) 4
(c) –2
(d) – 4

Question. The zeroes of a polynomial p(x) are precisely the x-coordinates of the points, where the graph of y = p(x) intersects the
(a) x – axis
(b) y – axis
(c) origin
(d) none of the above

Question. If α,β are the zeroes of the polynomials f(x) = x² – p(x + 1) – c, then (α +1)(β +1) =
(a) c – 1
(b) 1 – c
(c) c
(d) 1 + c

Question. A quadratic polynomial can have at most …….. zeroes
(a) 0
(b) 1
(c) 2
(d) 3

Question. A cubic polynomial can have at most …….. zeroes.
(a) 0
(b) 1
(c) 2
(d) 3

Question. Which are the zeroes of p(x) = x² – 1:
(a) 1, –1
(b) – 1, 2
(c) –2, 2
(d) –3, 3

Question. Which are the zeroes of p(x) = (x – 1)(x – 2):
(a) 1, –2
(b) – 1, 2
(c) 1, 2
(d) –1, –2

Question. Which of the following is a polynomial? 

Question. Which of the following is not a polynomial?