MCQs for Class 10 Maths Chapter 2: Polynomials

Q1: If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is

• 10
• -10
• 5
• -5

Q2: The number of polynomials having zeroes as –2 and 5 is

• 1
• 2
• 3
• more than 3

Q3: If the zeroes of the quadratic polynomial ax² + bx + c, c≠0 are equal, then

• c and b have opposite signs
• c and a have opposite signs
• c and b have same signs
• c and a have same signs

Q4: A polynomial of degree 3 is called

• a linear polynomial
• a quadratic polynomial
• a cubic polynomial
• a biquadratic polynomial

Q5: 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

• intersects y-axis
• intersects x-axis
• intersects y-axis or intersects x-axis
• none of these

Q6: The zeroes of the quadratic polynomial x² + 1750x + 175000 are

• both negative
• one positive and one negative
• both positive
• both equal

Q7: If one of the zeroes of the cubic polynomial x³ + ax² + bx + c is -1, then the product of the other two zeroes is

• b – a + 1
• b – a – 1
• a – b + 1
• a – b – 1

Q8: If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it

• has no linear term and the constant term is negative.
• has no linear term and the constant term is positive.
• can have a linear term but the constant term is negative.
• can have a linear term but the constant term is positive

Q9: If p(x) is a polynomial of degree one and p(a) = 0, then a is said to be:

• Zero of p(x)
• Value of p(x)
• Constant of p(x)
• None of the above

Q10: Dividend is equal to

• divisor × quotient + remainder
• divisor × quotient
• divisor × quotient – remainder
• divisor × quotient × remainder

Q11: What should be subtracted from x³ – 2x² + 4x + 1 to get 1?

• x³ – 2x² + 4x
• x³ – 2x² + 4 + 1
• -1
• 1

Q12: The zeroes of the quadratic polynomial x² + 99x + 127 are

• both positive
• both negative
• one positive and one negative
• both equal

Q13: If the zeroes of the quadratic polynomial ax² + bx + c, c ≠ 0 are equal, then

• c and a have opposite signs
• c and b have opposite signs
• c and a have the same sign
• c and b have the same sign

Q14: A polynomial of degree n has:

• Only one zero
• At least n zeroes
• More than n zeroes
• Atmost n zeroes

Q15: Find the quadratic polynomial whose zeros are 2 and -6

• x² + 4x + 12
• x² – 4x – 12
• x² + 4x – 12
• x² – 4x + 12

Q16: If a polynomial of degree 4 is divided by quadratic polynomial, the degree of the remainder is

• ≤ 1
• ≥ 1
• 2
• 4

Q17: If α, β are the zeroes of the polynomial x² – 16, then αβ(α + β) is

• 0
• 4
• -4
• 16

Q18: What is the quadratic polynomial whose sum and the product of zeroes is √2, ⅓ respectively?

• 3x² - 3√2x + 1
• 3x² + 3√2x + 1
• 3x² + 3√2x - 1
• None of the above

Q19: If α, β, γ are the zeroes of the cubic polynomial ax³ + bx² + cx + d then αβ + βγ + αγ is equal to

• −b/a
• b/a
• c/a
• d/a

Q20: Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is

• –c/a
• c/a
• 0
• 3

Q21: 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:

• Intersects x-axis
• Intersects y-axis
• Intersects y-axis or x-axis
• None of the above

Q22: 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?

• 5
• 6
• not defined
• -2

Q23: If α and 1/α are the zeroes of the polynomial ax² + bx + c, then value of c is

• 0
• a
• -a
• 1

Q24: The zeroes of x²–2x –8 are:

• (2,-4)
• (4,-2)
• (-2,-2)
• (-4,-4)

Q25: Every linear polynomial has — zero.

• Only one
• Two
• Three
• Four

Q26: Zeroes of p(x) = x² - 27 are:

• ±9√3
• ±3√3
• ±7√3
• None of the above

Q27: If the zeroes of the polynomial x³ – 3x² + x – 1 are st, s and st then value of s is

• 1
• -1
• 2
• -3

Q28: Graph of a quadratic polynomial is a ———

• Straight line
• Parabola
• Circle
• Hyperbola

Q29: If sum of the squares of zeroes of the quadratic polynomial 6x² + x + k is 25/36, the value of k is:

• 4
• – 4
• 2
• – 2

Q30: If p(x) is a polynomial of degree one and p(a) = 0, then a is said to be:

• Zero of p(x)
• Value of p(x)
• Constant of p(x)
• None of the above

Q31: The number of zeros of a cubic polynomial is

• 3
• at least 3
• 2
• at most 3

Q32: A polynomial p(x) of degree n has at most ——– zeroes.

• 1
• n
• n + 1
• n + 2

Q33: The sum and the product of the zeroes of polynomial 6x² – 5 respectively are

• 0, −6/5
• 0, 6/5
• 0, 5/6
• 0, −5/6

Q34: Sum and the product of zeroes of the polynomial x² + 7x + 10 is

• 10/7 and -10/7
• 7/10 and -7/10
• -7 and 10
• 7 and -10

Q35: If x³ + 1 is divided by x² + 5, then the possible degree of quotient is

• 0
• 1
• 2
• 3

Q36: The graph of the polynomial f(x) = 2x – 5 intersects the x – axis at

• (5/2, 0)
• (-5/2, 0)
• (-5/2, 5/2)
• (5/2, -5/2)

Q37: The value of p for which the polynomial x³ + 4x² – px + 8 is exactly divisible by (x – 2) is:

• 0
• 3
• 5
• 16

Q38: The zero of the linear polynomial ax + b is

• –a/b
• –b/a
• 0
• none