# MCQ Questions For Class 10 Polynomials

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) x2 – x -6
(b) x2 + x -6
(c) x2 + x +6
(d) x2 – x +6

B

Question. The zeroes of the quadratic polynomial x2 +99x +127 are
(a) both positive
(b) both negative
(c) one positive and one negative
(d) both equal

B

Question. If a, b are the zeroes of the polynomial f(x) = x2 -3x +2, then 1/α 1/β + equals to:
(a) 3
(b) –1
(c) 3/2
(d) – 3/2

C

Question. If the polynomial f(x) = ax3 + bx – c is divisible by the polynomial g(x) = x2 + bx + c, then the value of ab
is:
(a) 1/c
(b) 1
(c) –1
(d) none of these

B

Question. If f(x) = ax2 + 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

C

Question. If a,b are the zeroes of the polynomial f(x) = ax2 + bx + c, then 1/α2 1/β2 + equals to:
(a) b2-4ac/a2
(b) b2-2ac/c2
(c) b2-2ac/a2
(d) b2+2ac/c2

B

Question. If a and 1/α  are the zeroes of polynomial 4x2 -2x +(k- 4), the value of k is:
(a) 4
(b) 8
(c) 0
(d) none of these

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

C

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

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

C

Question. If the zeroes 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

D

Question. If p(x) = ax2+ 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

B

Question. Which of the following is a polynomial: C
(a) x2 + 1/x
(b) 2x2 -3√x +1
(c) 3x2 -3x +1
(d) x2 + x -2 +7

C

Question. The product and sum of zeroes of the quadratic polynomial ax2 + bx + c are respectively.
(a) b/a , c/a
(b) c/a , b/a
(c) c/b , 1
(d) c/a , -b/a

D

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) c/a
(c) 0
(d) -b/a

B

Question. A quadratic polynomial whose roots are –3 and 4 is
(a) x2 – x +12
(b) x2 + x +12
(c) x2/2 – x/2-6
(d) 2x2 +2x -24

C

Question. If one of the zeroes of the quadratic polynomial (k -1) x2 + kx +1 is –3, then the value of k is
(a) 4/3
(b) -4/3
(c) 2/3
(d) -2/3

A

Question. If the product of two zeroes of the polynomial p(x) = 2x3 +6x2 – 4x +9 is 3, then its third zero is
(a) -3/2
(b) 3/2
(c) -9/2
(d) 9/2

A

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.

A

Question. If a and b are zeroes of p(x) = x2 + x -1, then 1/α + 1/β + equals to
(a) –1
(b) 1
(c) 2
(d) 0

B

Question. If the zeroes of the quadratic polynomial ax2+ bx + c, c0 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

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

D

Question. If √(5/3) and -√(5/3) are two zeroes of the polynomial 3x4 +6x3 -2x2 -10x -5, then its other two zeroes are:
(a) –1, –1
(b) 1, –1
(c) 1, 1
(d) 3, –3

A

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.

A

Question. If a and b are zeroes of p(x) = x2 + x -1, then 1/α + 1/β + equals to
(a) –1
(b) 1
(c) 2
(d) 0

B

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

A

Question. A quadratic polynomial with 3 and 2 as the sum and product of its zeroes respectively is
(a) x2 +3x -2
(b) x2 -3x +2
(c) x2 -2x +3
(d) x2 -2x -3

B

Question. Given that two of the zeroes of the cubic polynomial ax3 + 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

C

Question. If the zeroes of the quadratic polynomial ax2 + 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

B

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) c/a
(c) 0
(d) -b/a

B

Question. Given that two of the zeroes of the cubic polynomial ax3 + bx2 + 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

C

Question. If the zeroes of the quadratic polynomial ax2 + 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

B

Question. The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0
(a) cannot both be positive
(b) cannot both be negative
(c) are always equal
(d) are always unequal

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

D

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

A

Question If one zero of the quadratic polynomial x2  -5x + k is –4 ,then the value of k is
(a) 36
(b) –36
(c) 18
(d) –18

B

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) x2  +8x +9

B

Question If one of the zeroes of the cubic polynomial x 3 + 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

A

Question If the zeroes 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

D

Question. The zeroes of the quadratic polynomial x2 + ax + b a, b > 0 are
(a) both positive
(b) both negative
(c) one positive one negative
(d) can’t say

B

Question. A quadratic polynomial, whose zeroes are 5 and –8 is
(a) x2 +13x – 40
(b) x2 + 4x -3
(c) x2 -3x + 40
(d) x2 +3x – 40

D

Question. The number of polynomials having exactly two zeroes 1 and –2 is
(a) 1
(b) 2
(c) 3
(d) infinitely many

A

Question. The degree of the remainder r(x) when p(x)= bx3 + 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

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?

No

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

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.

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)?

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?

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.

T

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

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)?

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.

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.

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)?

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.

True

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

T

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

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.

F

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

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.

No

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

No

Question. If the zeroes of the algebraic expression 3ax2 + 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) = x3 – ax2 + 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) = x4 – 2x3 – 18x2 – 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) = x2 + x + 1 and q (x) = x3 – 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) = ax2 + ax + b then the value of p4 + q4 is ______
(a) (a2 – 2bc)2 – b2c2/c4
(b) (a2 – 2bc)2 – 2b2c2/c4
(c) (b2 – 2ac)2 – a2c2/c4
(d) (b2 – 2ac)2 – 2a2c2/c4
(e) None of these

Ans.

B

Question.If the zeroes of the polynomial f(x) = ax3 + 3bx2 3cx + d are in A.P. then 2b3 + a2d is equal to _______
(a) a2 bc
(b) 3abc
(c) 2b2 ac
(d) abc
(e) None of these

Ans.

B

Question. If the LCM of p(x) and q(x) is a9 b9 then their HCF can be
(a) (a – b)
(b) (a2 + b2 + ab)
(c) a6 + b6 + a3b3
(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) = 3x4 + 6x3 – 2x2 – 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

As you most likely are aware as per the most recent syllabus, the first segment that you will find on your exam will be MCQs, so practice these MCQs and these will assist you with acquiring good marks.

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Our teachers have developed really good Multiple Choice Questions covering all important topics in each chapter which are expected to come in upcoming tests and exams, as MCQs are coming in all exams now therefore practice them carefully to get full understanding of topics and get good marks. Download the latest questions with multiple choice answers for Class 10th Polynomials in pdf or read online for free.

The above NCERT based MCQs for Class 10th Polynomials have been designed by our teachers in such a way that it will help you a lot to gain an understanding of each topic. These CBSE NCERT Class 10th Polynomials Multiple Choice Questions have been developed and are available free for benefit of Class 10 students.

a) MCQs will help the kids to strengthen concepts and improve marks in tests and exams.

b) Class 10th polynomials MCQ Questions have proven to further enhance the understanding and question solving skills.

c) Regular reading topic wise questions with choices will for sure develop very good hold over each chapter which will help in exam preparations.

d) It will be easy to revise all Polynomials chapters and faster revisions prior to class tests and exams.

Free Printable MCQs in PDF of CBSE Class 10th Polynomials are designed by our school teachers and provide best study material as per CBSE NCERT standards.

Where can I get MCQs for Polynomials ?

You can easily get MCQs for Polynomials from https://www.cbsencertsolutions.com

I want the latest MCQs based on this years syllabus ?

The MCQs for Class 10 Polynomials with Answers have been developed based on current NCERT textbook issued by CBSE.

Are all chapters covered ?

MCQs cover the topics of all chapters given in NCERT Book for Class 10 Polynomials.

Can I print these MCQs ?

Yes – These Multiple Choice Questions for Class 10 Polynomials with Answers are free to print and use them later.

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No – All MCQs for Polynomials are free to read for all students.