# MCQ Chapter 2 Polynomials Class 10 Mathematics

Please refer to Polynomials MCQ Questions Class 10 Mathematics below. These MCQ questions for Class 10 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Polynomials will help you to prepare for the exams and get more marks.

## Polynomials MCQ Questions Class 10 Mathematics

Please see solved MCQ Questions for Polynomials in Class 10 Mathematics. All questions and answers have been prepared by expert faculty of standard 10 based on the latest examination guidelines.

### MCQ Questions Class 10 Mathematics Polynomials

Question. If α,β are the zeros of the polynomial x2 − px + q, then α22 +β22 is equal to −
(a) p4/q2 +2 −4p2/q
(b) p4/q2 −2 +4p2/q
(c) p4/q2+2q−4p2/q
(d) None of these

A

Question. If a,b are the zeros of the polynomial x2 − px + 36 and α2 + β2 = 9, then p =
(a) ± 6
(b) ± 3
(c) ± 8
(d) ± 9

D

Question. If α,β are zeros of ax2 + bx + c, ac ≠ 0, then zeros of cx2 + bx + a are −
(a) − α − β
(b) α,1/ β
(c) β,1/ α
(d) 1/α,1 /β

D

Question. If x − 3 is a factor of x3 + 3x2 + 3x + p, then the value of p is
(a) 0
(b) −63
(c) 10
(d) None

B

Question. If 2 and 3 are the zeros of f(x) = 2x3 + mx2 − 13x + n, then the values of m and n are respectively −
(a) −5, − 30
(b) −5, 30
(c) 5, 30
(d) 5, − 30

B

Question. If a,b are the zeros of the polynomial 6x2 + 6px + p2, then the polynomial whose zeros are (α + β)2 and (α −β)2 is −
(a) 3x2 + 4p2x + p4
(b) 3x2 + 4p2x − p4
(c) 3x2 − 4p2x + p4
(d) None of these

C

Question. The value of ax2 + bx + c when x = 0 is 6. The remainder when dividing by x + 1 is 6. The remainderwhen dividing by x + 2 is 8. Then the sum of a, b and c is
(a) 0
(b) −1
(c) 10
(d) None

A

Question. If the G.C.D. of the polynomials x3 − 3x2 + px + 24 and x2 −7x + q is (x − 2), then the value of (p + q) is:
(a) 0
(b) 20
(c) −20
(d) 40

A

Question. The remainder of x4 + x− x2 + 2x + 3 when divided by x − 3 is
(a) 105
(b) 108
(c) 10
(d) None

B

Question. If the L.C.M. of two polynomials p(x) and q(x) is (x + 3)(x − 2)2(x − 6) and their H.C.F. is (x − 2).If p(x) = (x + 3)(x − 2)2, then q(x) =________
(a) (x + 3)((x − 2)
(b) x2 − 3x − 18
(c) x2 − 8x + 12
(d) none of these

C

Question. If α,β,γ are the zeros of the polynomial x3 + 4x + 1, then (α + β)−1 + (β + γ)−1 + (γ + α)−1 =
(a) 2
(b) 3
(c) 4
(d) 5

C

Question. If α,β are the roots of ax2 + bx + c and a + k, b + k are the roots of px2 + qx + r, then k =
(a) −1/2[a/b−p/q]
(b) [a/b−p/q]
(c) 1/2[b/a−q/p]
(d) (ab − pq)

C

Question. The condition that x3 − ax2 + bx − c = 0 may have two of the roots equal to each other but of opposite signs is :
(a) ab = c
(b) 2/3,a
(c) a2b = c
(d) None

A

Question. The remainder when x1999 is divided by x2 − 1 is
(a) − x
(b) 3x
(c) x
(d) None

C

Question. For the expression f(x) = x3 + ax2 + bx + c, if f(a) = f(b) = 0 and f(d) = f(0). The values of a, b & c are
(a) a = − 9, b = 20, c = − 12
(b) a = 9, b = 20, c = 12
(c) a = − 1, b = 2, c = − 3
(d) None of these

A

Question. If x2 − ax + b = 0 and x2 − px + q = 0 have a root in common and the second equation has equal roots, then
(a) b + q = 2ap
(b) b + q = ap /2
(c) b + q = ap
(d) None of these

B

Question. If f(x) = ax2 + bx + c is divided by (bx + c), then the remainder is_____.
(a) c2/b2
(b) ac2/b2 + 2c
(c) f(−c/b)
(d) ac2 +2b2c/b2

C

Question. ax4 + bx3 + cx2 + dx + e is exactly divisible by x2 − 1, when:
(a) a + b + c + e = 0
(b) a + c + e = 0
(c) a + b = 0
(d) a + c + e = b + d = 1

B

Question. If x + 1 is a factor of ax4 + bx3 + cx2 + dx + e = 0 then ____
(a) a + c + e = b + d
(b) a + b = c + d
(c) a + b + c + d + e = 0
(d) a + c + b = d + e

A

Question. If a3 −3a2b + 3ab2 − b3 is divided by (a − b), then the remainder is
(a) a2 − ab + b2
(b) a2 + ab + b2
(c) 1
(d) 0

D

Question. xn − yn is divisible by x + y, when n is_______.
(a) An odd positive integer
(b) An even positive integer
(c) An integer
(d) None of these

C

Question. If α,β are the zeros of the quadratic polynomial 4x2 − 4x + 1, then α3 + β3 is −
(a) 1/ 4
(b) 1/ 8
(c) 16
(d) 32

A

Question. If a + b = 4 and a3 + b3 = 44, then a,b are the zeros of the polynomial.
(a) 2x2 − 7x + 6
(b) 3x2 + 9x + 11
(c) 9x− 27x + 20
(d) 3x2 − 12x + 5

D

Question. If the sum of zeros of the polynomial p(x) = kx− 5x2 − 11x − 3 is 2, then k is equal to
(a) k = − 5/ 2
(b) k = 2/ 5
(c) k = 10
(d) k = 5/ 2

D

Question. If y = f(x) = mx + c; then f(y) in terms of x is
(a) mx + m + c
(b) m + mc + c
(c) m2x + mc + c
(d) m2x + m2c

C

Question. If 7 + 3x is a factor of 3x3 + 7x, then the remainder is
(a) 490/ 9
(b) −490/ 9
(c) 470/ 9
(d) None

B

Question. The remainder when f(x) = 3x4 + 2x3 −x2/3 −x/9 + 2/27 is divided by g(x) = x + 2/ 3 is
(a) −1
(b) 1
(c) 0
(d) −2

C

Question. f(x) = 3x5 + 11×4 + 90x− 19x + 53 is divided by x + 5 then the remainder is ______.
(a) 100
(b) −100
(c) −102
(d) 102

C

Question. If f(x) = 4x3 − 6x2 + 5x − 1 and α,β and γ are its zeros, then αβγ =
(a) 3/ 2
(b) 5/ 4
(c) −3/2
(d) 1/ 4

D

Question. Consider f(x) = 8x4 − 2x2 + 6x − 5 and a,b,g,d are it’s zeros then α + β + γ + δ =
(a) 1/ 4
(b) − 1/ 4
(c) −3/2
(d) None

D

Question. If (x − 3), (x −3) are factors of x− 4x2 − 3x + 18; then the other factor is
(a) x + 2
(b) x + 3
(c) x − 2
(d) x + 6

A

Question. The remainder when 1 + x + x2 + x3 + ……….+ x2006 is divided by x− 1 is
(a) 2005
(b) 2006
(c) 2007
(d) 2008

C

Question. If (x − 1), (x + 1) and (x − 2) are factors of x4 + (p − 3)x3 − (3p − 5)x2 + (2p − 9) x + 6 then the value of p is
(a) 1
(b) 2
(c) 3
(d) 4

D

Question. If f (−3/4)=0; then for f(x), which of the following is a factor?
(a) 3x − 4
(b) 4x + 3
(c) −3x + 4
(d) 4x − 3

B

Question. If the remainder when the polynomial f(x) is divided by x − 1, x + 1 are 6, 8 respectively then the remainder when f(x) is divided by (x − 1)(x + 1) is
(a) 7 − x
(b) 7 + x
(c) 8 − x
(d) 8 + x

A

Question. If a, b and g are the zeros of the polynomial f(x) = x3 + px2 − pqrx + r, then 1/αβ + 1/βγ +1/γα =
(a) r/p
(b) p/ r
(c) − p/ r
(d) − r/ p

B

Question. The coefficient of x in x2 + px + q was taken as 17 in place of 13 and it’s zeros were found to be − 2 and − 15. The zeros of the original polynomial are
(a) 3, 7
(b) − 3, 7
(c) − 3, − 7
(d) −3, − 10

D

Question. Let a, b be the zeros of the polynomial x2 − px + r and ,α/2, 2β be the zeros of x2− qx + r. Then the value of r is −
(a) 2/9 (p−q)(2q−p)
(b) 2/9 (q−p)(2p−q)
(c) 2/9 (q −2p)(2q−p)
(d) 2/9(2p−q)(2q−p)

D

Question. When x200 + 1 is divided by x2 + 1, the remainder is equal to −
(a) x + 2
(b) 2x − 1
(c) 2
(d) − 1

C

Question. If a (p + q)2 + 2bpq + c = 0 and also a(q + r)2 + 2bqr + c = 0 then pr is equal to −
(a) p2 + a/ c
(b) q2 +c/a
(c) p2 +q/b
(d) q2 +a/c

B

Question. If α, β and γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then 1/α +1/β +1/γ =
(a) −b/ a
(b) c/ d
(c) −c/d
(d) −c / a

C

Question. If a, b and g are the zeros of the polynomial f(x) = ax− bx2 + cx − d, then α2 +β2 + γ2 =
(a) b2 −ac/a2
(b) b2 +2ac/b2
(c) b2 −2ac/a
(d) b2 −2ac/a2

D

Question. If a,b and c are not all equal and a and b be the zeros of the polynomial ax2 + bx + c, then value of (1 + a + a2) (1 + b + b2) is :
(a) 0
(b) positive
(c) negative
(d) non-negative

D

Question. f(x) = 16x2 + 51x + 35 then one of the factors of f(x) is
(a) x − 1
(b) x + 3
(c) x − 3
(d) x + 1

D

Question. Find the remainder obtained when x2007 is divisible by x2 − 1.
(a) x2
(b) x
(c) x + 1
(d) −x

B

Question. If a polynomial 2x− 9x2 + 15x + p, when divided by (x − 2), leaves −p as remainder, then p is equal to
(a) −16
(b) −5
(c) 20
(d) 10

B

Question. If a, b and g are the zeros of the polynomial 2x3 − 6x2 − 4x + 30, then the value of (ab + bg + ga) is
(a) − 2
(b) 2
(c) 5
(d) − 30

A

Question. If ax3 + 9x2 + 4x − 1 is divided by (x + 2), the remainder is −6; then the value of ‘a’ is
(a) −3
(b) −2
(c) 0
(d) 33 8

D

Question. If c, d are zeros of x2 − 10ax − 11b and a, b are zeros of x2 − 10cx − 11d, then value of a + b + c + d is
(a) 1210
(b) − 1
(c) 2530
(d) − 11

A

Question. If the ratio of the roots of polynomial x2 + bx + c is the same as that of the ratio of the roots of x2 + qx + r, then
(a) br2 = qc2
(b) cq2 = rb2
(c) q2c2 = b2r2
(d) bq = rc

B

Question. The quadratic polynomial whose zeros are twice the zeros of 2x2 − 5x + 2 = 0 is −
(a) 8x2 − 10x + 2
(b) x2 − 5x + 4
(c) 2x2 − 5x + 2
(d) x2 − 10x + 6

B

Question. If α,β,γ are the zeros of the polynomial x3 − 3x + 11, then the polynomial whose zeros are (α+β), (β+γ) and (γ+α) is −
(a) x3 + 3x + 11
(b) x3 − 3x + 11
(c) x3 + 3x − 11
(d) x3 − 3x − 11

D

Question. If α,β,γ are such that α + β + γ = 2, α2 + β2 + γ2 = 6, α3 + β3 + γ3 = 8, then α4 + β4 + γ4 is equal to
(a) 10
(b) 12
(c) 18
(d) None

C

Question. If one zero of the polynomial ax2 + bx + c is posi- tive and the other negative then (a,b,c ∈R, a ≠ 0)
(a) a and b are of opposite signs.
(b) a and c are of opposite signs.
(c) b and c are of opposite signs.
(d) a,b,c are all of the same sign.

B

Question. A real number is said to be algebraic if it satisfies a polynomial equation with integral coefficients. Which of the following numbers is not algebraic :
(a) 2/ 3
(b) 2
(c) 0
(d) π

D

Question. If two zeroes of p(x)= 2x4 + x3 – 14x2 – 19x – 6 are –1 and –2, the other two zeroes are:
(a) 1/ 2 and – 3
(b) −1/ 2 and – 3
(c) −1/ 2 and 3
(d) none of these

C

Question. The graph of y = – 3x2 + 2x– 1 cuts the x-axis at :
(a) 1/ 3 and 0
(b) 1/ 3 and 1/ 3
(c) do not cut
(d) none of these

C

Question. The two zeroes of f(x) = x4– 6x3 – 26x2 + 138x – 35 are 2 ± √3 , the other two zeroes are :
(a) 7 and –5
(b) –7 and 5
(c) –7 and – 5
(d) none of these

A

Question. The zeroes of y = x2 + 7x + 12 are :
(a) 4 and – 3
(b) –4 and –3
(c) –4 and 3
(d) 4 and 3

B

Question. If the zeroes of f(x) = x3 – 3x2 + x + 1 are a – b, a, a + b, then value of a and b is :
(a) a =1, b = −√ 2
(b) a =1, b = −√2
(c) a =1, b =√2
(d) none of these

B

Question. The zeroes of f (x) = 4 √3x2 +5x − 2 √3 are :
(a) 2/√3 and −√3/4
(b) −/√32 and −√3/4
(c) −2/√3 and √3/4
(d) none of these

D

Question. The sum and product of zeroes of quadratic polynomial 3x2 – 8x + 12 is :
(a) −8/3 , 4
(b) 8/3 , 4
(c) −8/3 , −4
(d) none of these

B

Question. The graph of y = f (x) is given in figure (ii). How many zeroes are there of f (x)?

(a) 0
(b) 1
(c) 2
(d) many

B

Question. The number of polynomials having zeroes as –2 and 5 is
(a) 1
(b) 2
(c) 10
(d) infinite

D

Question. The solution of x2 + 6x + 9 = 0 is
(a) –1
(b) 3
(c) –3
(d) 1

C

Question. The graph of y = f (x) is given in figure (i), for some polynomial f (x). The number of zeroes of f (x) is

(a) 1
(b) 2
(c) 3
(d) many

C

Question. The value of k for which (–4) is a zero of the polynomial x2 – x – (2k + 2) is
(a) 2
(b) –6
(c) 9
(d) 8

C

Question. The graph of y = f (x) is given in figure (iii). How many zeroesare there of f (x)?

(a) 1
(b) 2
(c) 3
(d) None

D

Question. The zeroes of the quadratic equation 4s2 – 4s + 1 are
(a) 1/2 , 1/4
(b) 1/2 , 1/2
(c) 1/4 , 1/14
(d) 1/3 , 1/4

B

Question. The quadratic polynomial, sum of whose zeroes is 8 and their product is 12, is given by
(a) x2 – 8x + 12
(b) x2 + 8x – 12
(c) x2 – 5x + 7
(d) x2 + 5x – 7

A

Question. A quadratic polynomial whose product and sum of zeroes are −13/ 5 and 3/5 , respectively.
(a) k(x2 + 12x + 5)
(b) k[x2 – (8x) + (–9))
(c) k [x2 − (1/2 x) + ( −7/5)]
(d) k [x2 − (3/5 x) + (−13/5)]

D

Question. A quadratic polynomial whose zeroes are 1 and –3 is
(a) x2 + 3x – 2
(b) x2 + 5x – 5
(c) x2 + 2x – 3
(d) None of these

C

Question. The sum and product of zeroes of the quadratic equation given in example 3 are respectively
(a) 2, 3/4
(b) 0, 1/8
(c) 1, 1/4
(d) None of these

C

Question. The set of the zeroes of the polynomial x2 – 25, their sum and product is
(a) 4, 3; 7; 12
(b) –3, 3; 0; –9
(c) 5, –5; 0; –25
(d) None of these

C

Question. If the product of the zeroes of the polynomial ax2 – 6x – 6 is 4, then value of a is
(a) 1/8
(b) – 1/4
(c) 5/3
(d) –3/2

D

Question. If a, b are the zeroes of the polynomial 2x2 – 5x + 7, then a polynomial whose zeroes are 2α + 3β, 3α + 2β is
(a) k(x2 − 3/5 x + 21)
(b) k (x2 − 25/2 x + 41)
(c) k (x2 +9/2 x − 45 )
(d) None of these

B

Question. The value of k, if the sum of the zeroes of the polynomial x2 – (k + 6) x + 2 (2k – 1) is half of their product is
(a) 7
(b) 11
(c) 12
(d) None of these

A

Question. A quadratic equation x2 – 2x – 8 is given. The zeroes of it are
(a) –2 and 4
(b) 3 and 5
(c) 1 and 6
(d) None of these

A

Question. If the zeroes of the polynomial x2 + px + q are double in value to the zeroes of 2x2 – 5x – 3, the values of p and q are respectively
(a) 5, 6
(b) 4, 7
(c) –5, –6
(d) –4, –7

C

Question. The sum and product of the zeroes of the quadratic equation given in example 1 are respectively
(a) 2, 4
(b) 5, –8
(c) 6, 8
(d) 2, –8

D

Question. The remainder when f (x) = – 3x2 + x4 + 4x + 5 is divided by –x2 + 2 is
(a) 6
(b) 8
(c) 12
(d) none of these

D

Very Short Answer and Question :

Question. Find the common zero of x2 –1, x4 –1 and (x –1)2 ?

x + 1

Question. Write a polynomial whose sum and product of zeroes are 2 and –9 respectively.

x2 – 2x – 9

Question. If α, β are the zeroes of quadratic polynomial x2 – 3x + 2, form a quadratic polynomial whose zeroes are –α, and –β .

k (x2 + 3x + 2)

Question. Find the zeroes of the polynomial 9x2 – 25.

± 5/3

Question. For what value of x, both the polynomials p(x) – x2 – x – 6 and q(x) – x2 – 2x –15 becomes zero.

x = 3

Question. How many maximum zeroes will the polynomial 3x3 + 6x2 – 7 can have ?

3

Question. What should be added to the polynomial p(x) = x2 – 5x + 4, so that 2 is a zero of p(x)?

2

Question. If α and β are the zeroes of the polynomial x2 – 5x + 6, find the value of 1/α +1/β .

5/ 6

(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion : x3 + x has only one real zero.
Reason : A polynomial of nth degree must have n real zeroes.

C

Question. Assertion : Degree of a zero polynomial is not defined.
Reason: Degree of a non-zero constant polynomial is ‘0’.

B

Question. Assertion : Zeroes of f(x) = x2 – 4x – 5 are 5, – 1.
Reason : The polynomial whose zeroes are 2 + √3, 2 –√3 is x2 – 4x + 7.

C

Question. Assertion : x2 + 4x – 5 has two zeroes.
Reason : A quadratic polynomial can have at the most two zeroes.