These Polynomials Class 10 MCQ with Answers are Compulsory for the Class 10 Board Exam. According to the new guidelines of the CBSE Exam pattern, Objective type Questions or MCQ will be interrogated in the board exam. So, Students have the extraordinary chance to get some extra no. with only a couple of words. Practice this MCQ on Polynomials for Class 10 that are given below and make your concepts of the chapter strong.

Students can refer to the following Class 10th polynomials MCQ Questions with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here collection of multiple choice questions for Class 10th Polynomials covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

**Class 10th polynomials MCQ Questions with Answers**

We have provided below chapter wise Class 10th polynomials MCQ Questions with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Polynomials MCQs in Class 10 pdf download can be really scoring for students, you should go through all problems and MCQ Questions for Class 10 Maths provided below so that you are able to get more marks in your exams.

**Question. The quadratic polynomial having zeroes –3 and 2 is **

(a) x^{2} – x -6

(b) x^{2} + x -6

(c) x^{2} + x +6

(d) x^{2} – x +6

**Answer**

B

**Question. The zeroes 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. If a, b are the zeroes of the polynomial f(x) = x ^{2} -3x +2, then 1/α 1/β + equals to: **

(a) 3

(b) –1

(c) 3/2

(d) – 3/2

**Answer**

C

**Question. If the polynomial f(x) = ax ^{3} + bx – c is divisible by the polynomial g(x) = x^{2} + bx + c, then the value of ab **

is:

(a) 1/c

(b) 1

(c) –1

(d) none of these

**Answer**

B

**Question. If f(x) = ax ^{2} + bx + c has no real zeroes and a + b + c < 0, then: **

(a) c = 0

(b) c > 0

(c) c < 0

(d) none of these

**Answer**

C

**Question. If a,b are the zeroes of the polynomial f(x) = ax ^{2} + bx + c, then 1/α^{2} 1/β^{2} + equals to: **

(a) b

^{2}-4ac/a

^{2}

(b) b

^{2}-2ac/c

^{2}

(c) b

^{2}-2ac/a

^{2}

(d) b

^{2}+2ac/c

^{2}

**Answer**

B

**Question. If a and 1/α are the zeroes of polynomial 4x ^{2} -2x +(k- 4), the value of k is: **

(a) 4

(b) 8

(c) 0

(d) none of these

**Answer**

B

**Question. The zeroes of 3x 2 +10x +7 3 are: **

(a) 7, 3

(b) √3,7 √3

(c) -√ 3 -7/√3,

(d) none of these

**Answer**

C

**Question. If the sum of the zeroes of the polynomial f(x) = 2x ^{3} -3kx^{2} + 4x -5 is 6, then the value of k is: **

(a) 2

(b) 4

(c) –2

(d) –2

**Answer**

B

**Question. If one root of the polynomial p(y) = 5y ^{2} +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 zeroes of the quadratic polynomial x ^{2} +(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. If p(x) = ax ^{2}+ bx + c has no real zero and a + b + c < 0, then **

(a) c = 0

(b) c < 0

(c) c > 0

(d) none of these

**Answer**

B

**Question**. Which of the following is a polynomial: C

(a) x^{2} + 1/x

(b) 2x^{2} -3√x +1

(c) 3x^{2} -3x +1

(d) x^{2} + x ^{-2} +7

**Answer**

C

**Question**. The product and sum of zeroes of the quadratic polynomial ax^{2} + bx + c are respectively.

(a) b/a , c/a

(b) c/a , b/a

(c) c/b , 1

(d) c/a , -b/a

**Answer**

D

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

(a) -c/a

(b) c/a

(c) 0

(d) -b/a

**Answer**

B

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

(a) 4/3

(b) -4/3

(c) 2/3

(d) -2/3

**Answer**

A

**Question. If the product of two zeroes of the polynomial p(x) = 2x ^{3} +6x^{2} – 4x +9 is 3, then its third zero is **

(a) -3/2

(b) 3/2

(c) -9/2

(d) 9/2

**Answer**

A

**Question. If one of the zeroes of a quadratic polynomial of the form x ^{2} + 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

**Question. If a and b are zeroes of p(x) = x ^{2} + x -1, then 1/α + 1/β + equals to **

(a) –1

(b) 1

(c) 2

(d) 0

**Answer**

B

**Question. If the zeroes 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. 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**

D

**Question. If √(5/3) and -√(5/3) are two zeroes of the polynomial 3x ^{4} +6x^{3} -2x^{2} -10x -5, then its other two zeroes are: **

(a) –1, –1

(b) 1, –1

(c) 1, 1

(d) 3, –3

**Answer**

A

**Question. If one of the zeroes of a quadratic polynomial of the form x ^{2} + 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

**Question. If a and b are zeroes of p(x) = x ^{2} + x -1, then 1/α + 1/β + equals to **

(a) –1

(b) 1

(c) 2

(d) 0

**Answer**

B

**Question. If 5 is a zero of the quadratic polynomial x ^{2} – kx -15, then the value of k is **

(a) 2

(b) –2

(c) 4

(d) – 4

**Answer**

A

**Question. A quadratic polynomial with 3 and 2 as the sum and product of its zeroes 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 zeroes of the cubic polynomial ax ^{3} + bx 2 + cx + d 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. If the zeroes of the quadratic polynomial ax ^{2} + bx + c, c ¹ 0 are equal, then **

(a) c and a have opposite signs

(b) c and a have the same sign

(c) c and b have opposite signs

(d) c and b have the same sign

**Answer**

B

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

(a) -c/a

(b) c/a

(c) 0

(d) -b/a

**Answer**

B

**Question. Given that two of the zeroes of the cubic polynomial ax ^{3} + bx^{2} + cx + d 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. If the zeroes of the quadratic polynomial ax ^{2} + bx + c, c ¹ 0 are equal, then **

(a) c and a have opposite signs

(b) c and a have the same sign

(c) c and b have opposite signs

(d) c and b have the same sign

**Answer**

B

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

(a) cannot both be positive

(b) cannot both be negative

(c) are always equal

(d) are always unequal

**Answer**

A

**Question If a polynomial of degree 6 is divided by a polynomial of degree 2, then the degree of the quotient is **(a) less than 4

(b) less than 2

(c) equal to 2

(d) equal to 4

**Answer**

D

**Question If one of the zeroes of a quadratic polynomial of the form x ^{2} + 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**

A

**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 A quadratic polynomial with sum and product of its zeroes 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 If one of the zeroes of the cubic polynomial x 3 + ax ^{2} + 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

**Question If the zeroes of the quadratic polynomial x ^{2} +(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. The zeroes of the quadratic polynomial x ^{2} + ax + b a, b > 0 are **

(a) both positive

(b) both negative

(c) one positive one negative

(d) can’t say

**Answer**

B

**Question. A quadratic polynomial, whose zeroes 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**. The number of polynomials having exactly two zeroes 1 and –2 is

(a) 1

(b) 2

(c) 3

(d) infinitely many

**Answer**

A

**Question. The degree of the remainder r(x) when p(x)= bx ^{3} + cx + d is divided by a polynomial of degree 4 is **

(a) less than 4

(b) less than 3

(c) equal to 3

(d) less than or equal to 3

**Answer**

C

**Question. Can x 2 -1 be the quotient on division of x 6 +2x 3 + x -1 by a polynomial in x of degree 5? **

**Answer**

No** **

**Question. The only value of k for which the quadratic polynomial kx 2 + x + k has equal zeroes is 1/2. **

**Answer**

False

**Question. If all the zeroes of cubic polynomial are negative, what can you say about the signs of all the coefficient and the constant term? Give reason. **

**Answer**

Same sign

**Question. If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degrees of p(x) and g(x)? **

**Answer**

deg g(x) £ deg p(x)

**Question. If the graph of a polynomial intersects the x-axis at only one point can it be a quadratic polynomial? **

**Answer**

Yes

**Question. If the graph of a polynomial intersects the x-axis exactly at two points, it may not be quadratic polynomial. State true or false. Give reason.**

**Answer**

T

**Question. What will be the degree of quotient and remainder on division of x 3 +3x -5 by x 2 +1? Justify. **

**Answer**

Degree of Quotient = 1, Degree of Remainder = 1

**Question. If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degrees of p(x) and g(x)? **

**Answer**

deg g(x) £ deg p(x)

**Question. If all the zeroes of a cubic polynomial are negative, then all the coefficients and constant term of the polynomial have the same sign. **

**Answer**

True

**Question. If all three zeroes of a cubic polynomial x 3 + ax 2 – bx + c are positive, then at least one of a, b and c is non-negative. **

**Answer**

**False**

**Question. If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)? **

**Answer**

deg p(x) < deg g(x)

**Question. If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms. **

**Answer**

True

**Question. A linear polynomial can have atmost one zero. State true or false. **

**Answer**

T

**Question. A quadratic polynomial has at least one zero. State true or false. **

**Answer**

F

**Question. The only value of k for which the quadratic polynomial kx 2 + x + k has equal zeroes is 1/2 , state true or false. **

**Answer**

F

**Question. The degree of a cubic polynomial is at least 3. State true or false. Give reason. **

**Answer**

F, because it is equal to 3.

**Question. Can (x -2) be the remainder of a polynomial when divided by p(x) = 3x + 4? Justify. **

**Answer**

No

**Question. If two of the zeroes of a cubic polynomial are zero, then does it have linear and constant terms? Give reason. **

**Answer**

No

**Question.** If the zeroes of the algebraic expression 3ax^{2} + x(3b + 5a are -3/7 and -5/3 , then find the value of a/b

(a) 1/3

(b) 4/5

(c) 7/3

(d) 3

(e) None of these

## Ans.

B

**Question.** Solve

## Ans.

D

**Question.** If α,β,y are the zeroes of the polynomial p(x) = x^{3} – ax^{2} + bx – c then 1/αβ + 1/αβ + 1/αβ = __________

(a) a/b

(b) b/c

(c) a/c

(d) c/d

(e) None of these

## Ans.

C

**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

## Ans.

C

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

(a) c + b + 1

(b) a – b + 1

(c) a – b

(d) a + b

(e) None of these

## Ans.

C

**Question.** If p and q are the zeroes of the quadratic polynomial f(x) = ax^{2} + ax + b then the value of p^{4} + q^{4} is ______

(a) (a^{2} – 2bc)^{2} – b^{2}c^{2}/c^{4}

(b) (a^{2} – 2bc)^{2} – 2b^{2}c^{2}/c^{4}

(c) (b^{2 }– 2ac)^{2} – a^{2}c^{2}/c^{4}

(d) (b^{2} – 2ac)^{2} – 2a^{2}c^{2}/c^{4}

(e) None of these

## Ans.

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

## Ans.

B

**Question.** If the LCM of p(x) and q(x) is a^{9} b^{9} then their HCF can be

(a) (a – b)

(b) (a^{2} + b^{2} + ab)

(c) a^{6} + b^{6} + a^{3}b^{3}

(d) all the above

(e) none of these

## Ans.

D

**Question.**The graph of a polynomial f(x) is shown below:

**The number of real zeroes of the polynomial f(x) is _________**

(a) 1

(b) 2

(c) 3

(d) 4

(e) None of these

## Ans.

D

**Question.** If f(x) = 3x^{4 }+ 6x^{3} – 2x^{2 – }l0x – 5 and two of its zeroes are – 1, – 1, then the other two zeroes are _______

(a) √3/5 – √3/5

(b) √2/5 – √2/5

(c) √5/3 – √5/3

(d) √5/4 – √5/4

(e) None of these

## Ans.

C

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