# Polynomials MCQ Class 10 Mathematics

Please refer to Chapter 2 Polynomials MCQ Class 10 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 10 Mathematics. Students should refer to MCQ Questions for Class 10 Mathematics with Answers to score more marks in Grade 10 Mathematics exams. Students should read the chapter Polynomials and then attempt the following objective questions.

**MCQ Questions Class 10 Mathematics Chapter 2 Polynomials**

The Polynomials MCQ Class 10 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

** Question . In Fig. 2.2, the graph of the polynomial p(x) is given. The number of zeroes of the polynomial is **

(a) 1

(b) 2

(c) 3

(d) 0

**Answer**

B

** Question . Given that m + 2, where m is a positive integer, is a zero of the polynomial q(x)= x ^{2} – mx – 6 . Which of these is the value of m? **(a) 4

(b) 3

(c) 2

(d) 1

**Answer**

D

** Question . The quadratic polynomial, the sum of whose zeroes is – 5 and their product is 6, is **(a) x

^{2}+ 5x + 6

(b) x

^{2}– 5x + 6

(c) x

^{2}– 5x – 6

(d) – x

^{2}+ 5x + 6

**Answer**

A

** Question . If one of the zeroes of the quadratic polynomial x ^{2} + 3x + k is 2, then the value of k is **(a) 10

(b) – 10

(c) – 7

(d) – 2

**Answer**

B

** Question . The graph of a quadratic polynomial ax2 + bx + c = 0, having discriminant equal to zero, will touch x-axis at exactly how many points? **(a) one

(b) two

(c) three

(d) can’t say

**Answer**

A

** Question . The quadratic polynomial p(x) with –24 and 4 as a product and one of the zeros respectively is **(a) x

^{2}– 2x – 24

(b) x

^{2}+ 2x – 24

(c) x

^{2}+ 2x + 24

(d) Can’t be determined

**Answer**

B

** Question . The polynomial (x − a), where a > 0, is a factor of the polynomial q(x)= 4 √2 x – 2 √2 = . Which of these is a polynomial whose factor is (x-1/a) ? **(a) x

^{2}+ x + 6

(b) x

^{2}+ x – 6

(c) x

^{2}– 5x + 4

(d) x

^{2}+ 4x – 3

**Answer**

B

** Question . Which of these is a factor of the polynomial p(x)= x ^{3}+ 4x+ 5 **(a) (x + 1)

(b) (x – 1)

(c) (x + 3)

(d) (x – 3)

**Answer**

A

** Question . Consider the polynomial in z, p(z)= z ^{4} – 2z^{3} +3 . What is the value of the polynomial at z = −1? **(a) 6

(b) 5

(c) 4

(d) 3

**Answer**

A

**Question. The zeroes of the polynomial x ^{2} – 3x – m(m + 3) are **

(a) m, m + 3

(b) –m, m + 3

(c) m, – (m + 3)

(d) –m, – (m + 3)

**Answer**

B

**Question. If the zeroes of the quadratic polynomial x ^{2} + (a + 3) x+ b are 3 and – 4, then **

(a) a = 2, b = 6

(b) a = 2, b = 12

(c) a = 3, b = 4

(d) a = 4, b = 3

(e) None of these

**Answer**

B

**Question. If p(x) = x ^{2} + x + 1 and q(x) = x^{3} – x + 1 , then the HCF of p(a) – p(b) and q(a) **

(a) a + b + 1

(b) a – b + 1

(c) a + b

(d) a + b

(e) None of these

**Answer**

C

**Question. If on dividing the polynomial f(x)= x ^{3} – 4x^{2} +7x – 9 by a polynomial g(x), the quotient q(x) and the remainder r(x) are (x – 3) and (2x – 3) respectively, the polynomial g(x) is ____ **

(a) x

^{2}+ x + 1

(b) x

^{2}– x + 2

(c) 2x

^{2}+ x + 1

(d) 2x

^{2}– x + 2

(e) None of these

**Answer**

B

**Question. If the zeroes of the polynomial f(x) = ax ^{3} + 3bx^{2} + 3cx + d are in A.P. then 2b^{3} + a^{2}d is equal to _______ **

(a) a

^{2}bc

(b) 3abc

(c) 2b

^{2}ac

(d) abc

(e) None of these

**Answer**

B

**Question. If degree of both p(x) and [(p(x) + q(x)] is 15 then degree of q(x) can be **

(a) 12

(b) 10

(c) 15

(d) any one of the above

(e) None of these

**Answer**

D

**Question. If one of the zeroes of a cubic polynomial of the form x ^{3} + ax^{2} + bx + c is the negative of the other, then **

(a) a is of negative sign and b and c are of positive sign

(b) b is of negative sign and a and c are of positive sign

(c) a and c are of opposite signs and b is of negative sign

(d) a and b are of opposite signs and c is of positive sign

(e) None of these

**Answer**

C

**Question. Find the value of a – b so that 8x ^{4} + 14x^{3} – ax^{2} + bx + 2 is exactly divisible by 4x^{2} + 3x – 2 . **

(a) 4

(b) 6

(c) 9

(d) – 3

(e) None of these

**Answer**

C

**Question. If (x ^{2} + x – 1) is a factor of x^{4} + 9x^{3} + qx^{2} – 8x + 5 then find the values of p and q. **

(a) p = -3 , q = 4

(b) p = 4 , q = -3

(c) p = 2 , q = – 4

(d) p = -4 , q = 2

(e) None of these

**Answer**

B

**Question. If two zeroes of the polynomial f(x) = x ^{4} – 2x^{3} – 18x^{2} – 6x + 45 are -√3 and √3 , then find the sum of other two zeroes. **

(a) 0

(b) -1

(c) – 2

(d) 1

(e) None of these

**Answer**

C

**Question. A polynomial of degree n has ________ **

(a) two zeroes

(b) n zeroes

(c) atleast n zeroes

(d) atmost n zeroes

(e) None of these

**Answer**

D

**Question. The degree of polynomial having zeroes – 3 and 4 only is **

(a) 2

(b) 1

(c) more than 3

(d) 3

**Answer**

A

**Question. If one of the zeros of the cubic polynomial x ^{3} +ax^{2} + 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

**Question. The number of zeroes for a polynomial p(x) where graph of y = p(x) given in Fig. 2.1, is **

(a) 3

(b) 4

(c) 0

(d) 5

**Answer**

A

**Question. Consider the expression x ^{(m2-1)}+3x^{2}m , where m is a constant. For what value of m, will the expression be a cubic polynomial? **

(a) 1

(b) 2

(c) –1

(d) –2

**Answer**

B

**Question. The zeros of the quadratic polynomial ax ^{2} + 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

**Question. The zeros 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

**Question. A quadratic polynomial, whose zeros are – 3 and 4, is **

(a) x^{2} – x + 12

(b) x^{2} + x + 12

(c) x^{2}/2 –x/ 2– 6

(d) 2x^{2} + 2x – 24

**Answer**

C

**Question. The product of the zeros of the polynomial 4×2 + 3x + 7 is **

(a) 3/4

(b) –3/4

(c) 7/4

(d) –7/4

**Answer**

C

**Question. If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are 0, then the third zero is **

(a) b/a

(b) c/a

(c) –d/a

(d) –b/a

**Answer**

D

**Question. Which of these is a zero of the polynomials p(y)= 3y ^{3} – 16y – 8 ? **

(a) 2

(b) 8

(c) –2

(d) –8

**Answer**

C

**Question. If 2 and α are zeros of 2x ^{2} – 6x + 2 then the value of α is **

(a) 2

(b) 3

(c) 1

(d) 5

**Answer**

C

**Question. A quadratic polynomial with sum and product of its zeros as 8 and –9 respectively is **

(a) x^{2} –8x + 9

(b) x^{2} – 8x – 9

(c) x^{2} + 8x – 9

(d) x^{2} + 8x +9

**Answer**

B

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

**Answer**

D

**Question. If one zero of the quadratic polynomial x ^{2} –5x+ k + is – 4 , then the value of k is **

(a) 36

(b) –36

(c) 18

(d) –18

**Answer**

B

**Question. If one root of the polynomial p(y) = 5y2 + 13y + m is reciprocal of other, then the value of m is **

(a) 6

(b) 0

(c) 5

(d) 1/5

**Answer**

C

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

(a) cannot be a linear or a cubic polynomial

(b) can be a quadratic polynomial only

(c) can be a cubic or a quadratic polynomial

(d) can be a linear or a quadratic polynomial

**Answer**

C

**Question. The number of polynomials having zeros 1 and –2 is **

(a) 1

(b) 2

(c) 3

(d) more than 3

**Answer**

D

**Question. A quadratic polynomial, whose zeros are 5 and – 8 is **

(a) x^{2} + 13x – 40

(b) x^{2} + 4x – 3

(c) x^{2} – 3x + 40

(d) x^{2} + 3x – 40

**Answer**

D

**Question. A quadratic polynomial with 3 and 2 as the sum and product of its zeros respectively is **

(a) x^{2} + 3x – 2

(b) x^{2} – 3x + 2

(c) x^{2} – 2x + 3

(d) x^{2} – 2x – 3

**Answer**

B

**Question. Given that two of the zeros of the cubic polynomial ax bx cx d 3 2 + + + are 0, the value of c is **

(a) less than 0

(b) greater than 0

(c) equal to 0

(d) can’t say

**Answer**

C

**Question. Which of the following graphs could be for the simple polynomial x ^{2} ? **

**Answer**

C

**Question. Prashant claims that the polynomial p(x) = mxa + x ^{2}b (a > 2b) has 4b zeroes. For Prashant’s claim to be correct, which of these must be true? **

(a) a = 2 or a = 4b

(b) a = 4b

(c) m = 2b

(d) m = 4b

**Answer**

B

**Question. Product of zeros of a cubic polynomial is **

(a) –d/a

(b) c/b

(c) d/b

(d) –b/a

**Answer**

A

**Question. If one of the zeros of the quadratic polynomial (k – 1) x ^{2} + k x + 1 is – 3, then the value of k is **

(a) 3/ 4

(b) –4/3

(c) 2/3

(d) –2/3

**Answer**

A

**Question. If one of the zeros of a quadratic polynomial of the form x ax b 2+ + 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

**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**

A

**Question. Given that one of the zeroes of the cubic polynomial ax bx cx d 3 2 + + + is zero, then product of the other two zeros is **

(a) – c /a

(b) c/a

(c) 0

(d) –b/a

**Answer**

B

**Question. The zeros of the quadratic polynomial x ^{2}+kx+k,k≠0 **

(a) both cannot be positive

(b) both cannot be negative

(c) are always equal

(d) are always unequal

**Answer**

A

**Question. If the zeros of the quadratic polynomial x2(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

Question. Which of the **following** statements is correct?

(a) A polynomial of degree 3 has two zeroes

(b) A polynomial of degree 4 has four zeroes

(c) A polynomial of degree 5 has six zeroes

(d) A polynomial of degree 6 has five zeroes

**Answer**

B

**Question. The zeros of the quadratic polynomial x ax b, a,b > 0 2+ + are **

(a) both positive

(b) both negative

(c) one positive one negative

(d) can’t say

**Answer**

B

**Question. The number of polynomials having zeros as – 2 and 5 is **

(a) 1

(b) 2

(c) 3

(d) more than 3

**Answer**

D

**Question. Quadratic polynomial having zeroes a and b is **

(a) x^{2} – (αβ)x + (α + β)

(b) x^{2} – (α + β)x + αβ

(c) x^{2} − α/β x + α β

(d) None of these

**Answer**

B

**Question. The value of k such that the polynomial x ^{2} – (k + 6) x + 2(2k – 1) has sum of its zeros equal to half of their product is **

(a) 3

(b) 5

(c) 7

(d) None of these

**Answer**

C

**Question. If one zero of the quadratic polynomial x ^{2} – 5x – 6 is 6, then other zero is **

(a) 0

(b) 1

(c) –1

(d) 2

**Answer**

C

**Question. If a, b are the zeroes of the polynomial 2y ^{2} + 7y + 5, the value of α + β + αβ is **

(a) 0

(b) 1

(c) –1

(d) 2

**Answer**

C

**Question. A quadratic polynomial, the sum and product of whose zeroes and (–3) and 2 respectively is **

(a) x^{2} + 3x + 2

(b) x^{2} – 3x + 2

(c) x^{2} + 3x – 2

(d) None of these

**Answer**

A

**Question. The zeroes of the quadratic polynomial x2 + 7x + 10 are **

(a) –2, –5

(b) 2, 5

(c) –3, –8

(d) 3, 8

**Answer**

A

**Question. If the sum of the zeroes of the quadratic polynomial 3x ^{2} – kx + 6 is 3, then the value of k is **

(a) 3

(b) 6

(c) 9

(d) 0

**Answer**

D

**Question. If two zeroes of the polynomial p(x) = x ^{3} – 4x^{2} – 3x + 12 are √3 and − √3 , then its third zero is **

(a) √2

(b) √5

(c) 5

(d) 4

**Answer**

D

**Question. If 2 and –3 are the zeroes of the quadratic polynomial x2 + (a + 1) x + b; then the values of a and b respectively are **

(a) 0, –6

(b) 0, 0

(c) 6, –6

(d) 2, –3

**Answer**

A

**Question. If one of the zeroes of quadratic polynomial (k – 1) x ^{2} + kx + 1 is –3, then k = **

(a) 4/3

(b) – 4/3

(c) 2/3

(d) 3/2

**Answer**

A

**Question. Sum of the zeroes of the polynomial x ^{2} + 7x + 10 are **

(a) 7

(b) – 7

(c) 10

(d) – 10

**Answer**

B

**Question. The quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is **

(a) x^{2} + 5x + 6

(b) x^{2} – 5x + 6

(c) x^{2} – 5x – 6

(d) –x^{2} + 5x + 6

**Answer**

A

**Question. If a and b are the zeroes of the polynomial ax ^{2} + bx + c; then the value of a2 + b2 is **

(a) b

^{2}− ca/a

^{2}

(b) b

^{2}−2ca/a

^{2}

(c) b

^{2}+ ca/a

^{2}

(d) b

^{2}+ 2ca/a

^{2}

**Answer**

B

**Question. A quadratic polynomial whose zeroes are 5 − 3 √2 and 5 + 3 √2 is **

(a) x^{2} – 10x + 7

(b) x^{2} + 10x + 7

(c) x^{2} – 5x + 9

(d) x^{2} + 5x – 9

**Answer**

A

**Question. A quadratic polynomial, whose sum of zeroes is 2 and product is –8 is **

(a) x^{2} – 3x – 3

(b) x^{2} + 2x + 8

(c) x^{2} + 3x + 3

(d) x^{2} – 2x – 8

**Answer**

D

**Question. The other zero of the polynomial 2x ^{3} + x^{2} – 6x – 3, if two of its zeroes are − 3 and 3 is **

(a) 1/ 2

(b) – 1/ 2

(c) 1/ 3

(d) – 1/ 3

**Answer**

B

**Question. If a and b are the zeroes of the polynomial 4x ^{2} + 3x + 7, the value of 1/ α + 1/β is **

(a) − 1/ 2

(b) − 5/ 2

(c) − 3 /7

(d) 3/ 7

**Answer**

C

**Question. If one zero of the polynomial (a ^{2} + 9)x^{2} + 13x + 6a is reciprocal of the other, then ‘a’ is **

(a) 1

(b) 3

(c) 12

(d) 19

**Answer**

B

**Question. If a and b are zeroes of a polynomial x ^{2} + 6x + 9, then a polynomial whose zeroes are –α and –β is **

(a) x

^{2}– 6x + 9

(b) x

^{2}+ 6x – 9

(c) x

^{2}+ 5x + 4

(d) None of these

**Answer**

A

**Question. Quadratic polynomial 2x ^{2} – 3x + 1 has zeroes as α and β. A quadratic polynomial whose zeroes are 3a and 3b is **

(a) k/ 2 (3x

^{2}+ 5x – 5)

(b) k/ 2 (3x

^{2}– 5x + 5)

(c) k /2 (2x

^{2}+ 9x + 9)

(d) k /2 (2x

^{2}– 9x + 9)

**Answer**

D

**Question. The zeores of the quadratic polynomial 6x ^{2} – 3 – 7x are **

(a) 3/ 2, −1/ 3

(b) 2/ 3 , –3

(c) 3 /5 ,−3 /7

(d) None of these

**Answer**

A

**Question. The zeroes of the quadratic polynomial 4x ^{2} – 4x – 3 are **

(a) 3/ 2, −1/ 3

(b) 3/ 2, −1/ 2

(c) 2/ 5, −2/ 5

(d) None of these

**Answer**

B

**Question. A quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial : f(x) = ax ^{2} + bx + c, a ≠ 0, c ≠ 0 is **

(a) 1/ c (cx

^{2}+ bx + a)

(b) 1/ c (cx

^{2}– bx + a)

(c) 1/ c (cx

^{2}– bx – a)

(d) 1/ c (–cx

^{2}+ bx + a)

**Answer**

A

**Question. If α, β are the zeroes of the polynomial x ^{2} – 4x + 3, a quadratic polynomial whose zeroes are 3α and 3β is **

(a) x

^{2}+ 8x + 17

(b) x

^{2}+ 12x + 27

(c) x

^{2}– 12x + 27

(d) x

^{2}– 8x + 17

**Answer**

C

**Question. If α and β are the zeroes of the polynomial 5x ^{2} – 7x – 2, the sum of the reciprocals of zeroes is **

(a) 7 2

(b) − 7 2

(c) 5 9

(d) – 5 9

**Answer**

B

**Question. In the following questions, a statement of assertion (A) is followed by a statement reason (R). Choose the correct choice as: **

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

1. Assertion (A): If one zero of polynomial p(x) = (k^{2} + 4)x^{2} + 13x + 4k is reciprocal of each other, then k = 2.

Reason (R): If (x – a) is a factor of p(x), then p(a) = 0, i.e. a is a zero of p(x).

2. Assertion (A): If both zeroes of the quadratic polynomial x^{2} –2kx + 2 are equal in magnitude but opposite in sign, then value of k is 1/ 2 .

Reason (R): Sum of zeroes of a quadratic polynomial ax^{2} + bx + c is − b /a

**Answer**

**1. (B) , 2. (D)**

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