CBSE Class 10 Mathematics Polynomials MCQs 

Refer to CBSE Class 10 Mathematics Polynomials MCQs Set A provided below available for download in Pdf. The MCQ Questions for Class 10 Mathematics with answers are aligned as per the latest syllabus and exam pattern suggested by CBSE, NCERT and KVS. Chapter 2 Polynomials Class 10 MCQ are an important part of exams for Class 10 Mathematics and if practiced properly can help you to improve your understanding and get higher marks. Refer to more Chapter-wise MCQs for CBSE Class 10 Mathematics and also download more latest study material for all subjects

MCQ for Class 10 Mathematics Chapter 2 Polynomials

Class 10 Mathematics students should refer to the following multiple-choice questions with answers for Chapter 2 Polynomials in Class 10.

Chapter 2 Polynomials MCQ Questions Class 10 Mathematics with Answers

 

MCQs on Polynomials

1. If one zero of the quadratic polynomial $x^2 + 3x + k$ is 2, then the value of $k$ is:
   A) 10   B) –10   C) 5   D) –5
   Answer: B) –10

2. Given that two of the zeroes of the cubic polynomial $ax^3 + bx^2 + cx + d$ are 0, the third zero is:
   A) $-\frac{b}{a}$   B) $-\frac{c}{b}$   C) $-\frac{d}{c}$   D) None of these
   Answer: A) $-\frac{b}{a}$

3. If one of the zeroes of the quadratic polynomial $(k – 1)x^2 + kx + 1$ is –3, then the value of $k$ is:
   A) 2   B) –2   C) 1   D) –1
   Answer: A) 2

4. A quadratic polynomial whose zeros are –3 and 4 is:
   A) $x^2 - x + 12$   B) $x^2 + x + 12$   C) $\frac{x^{2}}{2} - \frac{x}{2} - 6$   D) $2x^2 + 2x – 24$
   Answer: C) $\frac{x^{2}}{2} - \frac{x}{2} - 6$

5. 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) $a = 0,\; b = -6$

6. The number of polynomials having zeroes as –2 and 5 is:
   A) 1   B) 2   C) 3   D) more than 3
   Answer: D) more than 3

7. If one zero of the quadratic polynomial $x^2 + kx + k$, $k \neq 0$, then:
   A) zeros cannot both be positive   B) zeros cannot both be negative   C) are always unequal   D) are always equal
   Answer: A) cannot both be positive

8. If the zeroes of a quadratic polynomial $ax^2 + bx + c$, $c \neq 0$, 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) $c$ and $a$ have the same sign

9. If one of the zeroes of a quadratic polynomial of the form $x^2 + ax + b$ is the negative of the other, then:
   A) it has no linear term and the constant term is negative   B) it 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) it has no linear term and the constant term is negative

10. The zeroes of the quadratic polynomial $x^2 – 18x + 81$ are:
    A) both negative   B) one positive and one negative   C) both positive and unequal   D) both equal and positive
    Answer: D) both equal and positive

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 : 2

 

Question : A quadratic polynomial with 3 and 2 as the sum and product of its zeroes respectively is

a) x² -3x +2

b) x² -2x +2

c) x² -2x -2

d) None of these

Answer :  x² -3x +2

 

Question : A quadratic polynomial, whose zeroes are 5 and –8 is

a) x² +3x - 40

b) None of these

c) x² -3x - 40

d) x² -13x - 40

Answer :  x² +3x - 40

 

Question : The number of polynomials having exactly two zeroes 1 and –2 is

a) 1

b) 2

c) 3

d) infinitely many

Answer : 1

 

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) 0

c) -b/a

d) -c/a

Answer : c/a

 

Question :  Given that two of the zeroes of the cubic polynomial ax 3 + bx² + cx + d are 0, the value of c is

a) equal to 0

b) can’t say

c) greater than 0

d) less than 0

Answer : equal to 0

 

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

a) c and a have the same sign

b) c and b have the same sign

c) c and a have opposite signs

d) c and b have opposite signs

Answer : c and a have the same sign

 

Question :  The zeroes of the quadratic polynomial x² + kx + k, k ¹ 0

a) cannot both be positive

b) are always equal

c) cannot both be negative

d) are always unequal

Answer : cannot both be positive

 

Question :  The zeroes of the quadratic polynomial x² + ax + b a, b > 0 are

a) both negative

b) both positive

c) one positive one negative

d) can’t say

Answer : both negative

 

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

a) can be a cubic or a quadratic polynomial

b) cannot be a linear or a cubic polynomial

c) can be a quadratic polynomial only

d) can be a linear or a quadratic polynomial

Answer : can be a cubic or a quadratic polynomial

 

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

a) both negative

b) both equal

c) both positive

d) one positive and one negative

Answer : both negative

 

Question : If ‘a’ and ‘b’ are unequal and x² + ax + b and x² + bx + a have a common factor, then a + b is equal to

a) –1 

b) 0 

c) 1 

d) –2

 

Answer : A

 

Question : Find the zeros of x(x - 3)

a) 1,3 

b) 0, 2 

c) 0, 3 

d) 2, 1
 

Answer : C

 

Question : Find the zeroes of (x+2) (2x-1)

a) –2, 1/2

b) 2,-1/2

c) –2, 1 

d) 2, -1

 

Answer : A

 

Question : Which of the following is a zero of 3x² - 5x - 2?

a) 2 

b) 1 

c) 4 

d) 3
 

Answer : A

 

Question : The value of 6a + 11 b , if x³ – 6x² + ax + b is exactly divisible by (x² – 3x + 2) is

a) 0 

b) 132 

c) 66 

d) – 66
 

Answer : A

 

Question : If α" role="presentation" style="display: inline-table; line-height: normal; font-size: 17.6px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: Tahoma, Arial, serif; position: relative;">α

, β, γ are the zeroes of the polynomial x³ - 6x² - x + 30 , then the value of (αβ + βγ+ γα) is-

a) –1 

b) 1 

c) -5 

d) 30
 

Answer : A

 

Question : If –2 and 3 are the zeroes of the quadratic polynomial x² + (a +1)x + b , then

a) a = –2, b = 6 

b) a = 2, b = – 6 

c) a = –2, b = –6 

d) a = 2, b = 6
Answer : C

 

Question : If α, β be the zeroes of the polynomial x² - 8x + k such that α² + β² = 40 , then k =?

a) 6 

b) 9 

c) 12

d) –12
 

Answer : C

 

Question : If α, β be the zeroes of the polynomial 2x² + 5x + k such that 4 α2 + β² +α,β = 21/4 , then k =?

a) 3 

b) –3 

c) –2 

d) 2
 

Answer : D

 

Question : How many polynomials are there having 4 and –2 as zeroes?

a) One 

b) Two 

c) Three 

d) More than three

 

Answer : D

Question. The value of k for which (–4) is a zero of the polynomial x2 – x – (2k +2) is
(a) 3
(b) 9
(c) 6
(d) –1

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

(a) c and a have opposite sign
(b) c and b have opposite sign
(c) c and a have the same sign
(d) c and b have the same sign

Question. The number of zeroes of the polynomial from the graph is
(a) 0
(b) 1
(c) 2
(d) 3

Question. If one of the zero of the quadratic polynomial x² +3x + k is 2, then the value of k is
(a) 10
(b) –10
(c) 5
(d) –5

Question. A quadratic polynomial whose zeroes are –3 and 4 is
(a) x² – x +12
(b) x² +x + 12
(c) 2x² + 2x – 24.
(d) none of the above.

Question. The relationship between the zeroes and coefficients of the quadratic polynomial ax² + bx + c is
(a) α + β = c/a
(b) α + β = -b/a
(c) α + β =-c/a
(d) α + β = b/a

Question. The zeroes of the polynomial x² + 7x + 10 are
(a) 2 and 5
(b) –2 and 5
(c) –2 and –5
(d) 2 and –5

Question. The relationship between the zeroes and coefficients of the quadratic polynomial ax² + bx + c is
(a) α.β = c/a
(b) α.β = -b/a
(c) α.β = -c/a
(d) α.β = b/a

Question. The zeroes of the polynomial x² – 3 are
(a) 2 and 5
(b) –2 and 5
(c) –2 and –5
(d) none of the above

Question. The number of zeroes of the polynomial from the graph is
(a) 0
(b) 1
(c) 2
(d) 3

Question. A quadratic polynomial whose sum and product of zeroes are –3 and 2 is 

(a) x² – 3x +2
(b) x² + 3x + 2
(c) x² + 2x – 3.
(d) x² + 2x + 3.

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 unequal
(d) are always equal

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

a)

b)

c)

d)

Answer :

Question :

a) –1, –1

b) 1, –1

c) 1, 1

d) 3, –3

Answer : –1, –1

Question : Which of the following is a polynomial

a) 3x² -3x +1

b) x² + x^-2 +7

c) 2x² -3x +1

d) None of these

Answer :  3x² -3x +1

Question :  If one zero of the quadratic polynomial x² -5x + k is –4 ,then the value of k is

a) –36

b) 18

c) –18

d) 36

Answer : –36

Question :  If the zeroes of the quadratic polynomial x² +(a +1)x + b are 2 and –3, then

a) a = 0, b = -6

b) a = 2, b = -6

c) a = 5, b = -1

d) a = -7, b = -1

Answer : a = 0, b = -6

Question : If a polynomial of degree 6 is divided by a polynomial of degree 2, then the degree of the

a) equal to 4

b) equal to 2

c) less than 2

d) less than 4

Answer : equal to 4

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

Answer : has no linear term and the constant term is negative

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) None of these

Answer :  x² -8x -9

Question :  If one of the zeroes of the cubic polynomial x³ + 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

Answer : a - b -1

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

Answer :  x² + x -6

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

a) c and a have the same sign

b) c and a have opposite signs

c) c and b have opposite signs

d) c and b have the same sign

Answer : c and a have the same sign

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

Answer : has no linear term and the constant term is negative.

Question :  If the zeroes of the quadratic polynomial x² +(a +1) x + b are 2 and –3, then

a) a = 0, b = -6

b) a = 2, b = -6

c) a = 5, b = -1

d) a = -7, b = -1

Answer : a = 0, b = -6

Question :  If f(x) = ax² + bx + c has no real zeroes and a + b + c < 0, then

a) c > 0

b) c < 0

c) none of these

d) c = 0

Answer : c > 0