# MCQs for Mathematics Class 10 with Answers Chapter 2 Polynomials

Students of class 10 Mathematics should refer to MCQ Questions Class 10 Mathematics Polynomials with answers provided here which is an important chapter in Class 10 Mathematics NCERT textbook. These MCQ for Class 10 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 10 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 10 Mathematics examination

## Chapter 2 Polynomials MCQ with Answers Class 10 Mathematics

MCQ Questions Class 10 Mathematics Polynomials provided below have been prepared by expert teachers of grade 10. These objective questions with solutions are expected to come in the upcoming Standard 10 examinations. Learn the below provided MCQ questions to get better marks in examinations.

Question. If α, s are the zeroes of p(x) = 2x² – 5x + 7, write a polynomial with zeroes 2α+3s and 3α+2s.
(a) k(x² + x – 41)
(b) k(x² – x + 41)
(c) k(x² – x – 41)
(d) k(- x² + x + 41)

B

Question. If sum of the two zeroes of a cubic polynomial x³ – ax² + bx – c, is zero, then which of thefollowing is true:
(a) ab = c
(b) a – b = c
(c) ab = c/2
(d) a = b/c

A

Question. If the polynomials ax³ + 4x² + 3x – 4 and x³ – 4x + a, leave the same remainder when divided by(x – 3), then value of a is :
(a) 2b
(b) – 1
(c) 1
(d) – 2b

B

Question. If p(x) = 2x⁴ – ax³ + 4x² + 2x + 1 is a. multiple of 1 – 2x, then find the value of a :
(a) 25
(b) 1/2
(c) -1/2
(d) 8

A

Question. If -2 is a zero of p(x) = (ax³ + bx² + x – 6) and p(x) leaves a remainder 4 when divided by (x – 2),then the values of a and b are (respectively):
(a)a = 2,b = 2
(b) a = 0,b = – 2
(c) a = 0, b = 2
(d) a = 0, b = 0

C

Question. If 2 is a zero of p(x) = x² + 3x + k, find k:
(a) 10
(b) 5
(c) – 3
(d) – 10

D

Question. Given that two of the zeroes of the polynomial, x³ + px² + rx + s are 0, then third zero
(a) 0
(b) p/r
(c) -p/r
(d) p/q

C

Question. If x 101 + 1001 is divided by x + 1, then remainder is:
(a) 0
(b) 1
(c) 1490
(d) 1000

D

Question. If one zero of the quadratic polynomial x2 + 5x + k is 3 then second zero of this polynomial is ______
(a) 5
(b) – 3
(c) – 5
(d) – 8
(e) None of these

D

Question. If α & β are the zeroes of the polynomial x2 + 6x – k such that 2β + α = 11 then k is equal to
(a) 18
(b) – 23
(c) 391
(d)- 391
(e) None of these

C

Question. See the graph given below:

Based on these graphs, identify the correct statement among the following:
(a) In case ii, the quadratic polynomial ax2 + bx + c has two distinct zeroes.
(b) In case i, the quadratic polynomial ax2 + bx + c has two equal zeroes.
(c) In case iii, the quadratic polynomial has no zero.
(d) All the above
(e) None of these

C

Question. If p and q are the zeroes of the quadratic polynomial f(x) = cx2 + ax + b then the value of p4 + q4 is ____

B

Question. If the zeroes of the algebraic expression 3ax2 + x (3b + 5b) + 5b 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

B

Question. Solve p2(q – r)2/(p + r)2 – q2 + q2 – (p – r)2/(p + q)2 – r2 + r2 – (p – q)2/(q + r)2 – p2 .
(a) 1/ p + q + r
(b) p + q + r
(c) 0
(d) 1
(e) None of these

D

Question. If two zeroes of the cubic polynomial px2 + qx2 + rx + s are 0, then the third zero is _________
(a) p/q
(b) -p/q
(c) -p/q
(d) 0
(e) None of these

C

Question. If α , β , ϒ are the zeroes of the polynomial p(x) = x3 – ax2 + bx – c , than 1/αβ + 1/βϒ + 1/αϒ = __________
(a) a/b
(b) b/c
(c) a/c
(d) c/d
(e) None of these

C

Question. If the zeroes of a quadratic polynomial ax2 + bx + c are both negative, then
(a) a is positive., b and c are negative
(b) a is negative/ b and c are positive
(c) a and c are negative, b is positive
(d) a, b and c all have the same sign
(e) None of these

D

Question. If the zeroes of the polynomial x3 – 15x2 + 66x – 80 are α , β & ϒ and it is also given that 2β = α + ϒ then
(a) α = 4
(b) ϒ = 3
(c) ϒ = 7
(d) α = 2
(e) None of these

D

Question. The zeroes of the quadratic polynomial x 2 + 1750x + 175000 are
(a) both negative
(b) one positive and one negative
(c) both positive
(d) both equal

A

Question. sum of the squares of the zeroes of the polynomial p(x) = x² + 7x – k is 25, find k.
(a) 12
(b) 49
(c) – 24
(d) – 12

D

Question. If one zero of 3x² – 8x + 2k + 1 is seven times the other, find k.
(a) 2/
(b) 1/3
(c) 4/3
(d) 5/3

A

Question. If one zero of a polynomial p(x) = ax² + bx + c(a ≠ 0) is zero, then, which of the following iscorrect:
(a) b = 0
(b) c = 0
(c) other zero is also zero
(d) Nothing can be said about p(x).

B

Question. Find a and b so that the polynomial 6x⁴ + 8x³ – 5x² + ax + b is exactly divisible by 2x² – 5.
(a) a = 20, b = – 25
(b) a = 4, b = – 5
(c) a = 20, b = 5
(d) a = – 20, b = – 25

D

Question. If the point (5,0), (0-2) and (3,6) lie on the graph of a polynomial. Then which of the following isa zero of the polynomial?
(a) 5
(b) 6
(c) not defined
(d) -2

A

Question. If a, s are the zeroes of p(x) = 2x² + 5x + k such that, α²+ s²+ αs =21/4 , then k equals,
(a) 12
(b) 4
(c) 2
(d) – 12

C

Question. If α, s are the zeroes of x² – lx + m, then α /s s/α
(a) l ² – 2 m/m
(b) l ² + 2 m/m
(c) l – 2 m/ m
(d) l² – 2m

A

Question. If α, s are the zeroes of x² + px + q, then a polynomial having zeroes and is,
(a) x² + px + q
(b) x² + qx + p
(c) px² + qx + 1
(d) qx² + px +1

D

Question. Find the number of zeros in the graph given:
(a) 3
(b) 2
(c) 1
(d) 0

B

Question. Write the zero of the polynomial p(x), whose graph is given :
(a) 1
(b) 0
(c) – 1
(d) – 2

B

Question. If α, s, v are the zeros of the polynomial 2x³ – x² + 3x -1, find the value of (αsv) + (αs + sv + vα).
(a) 2
(b) 3/2
(c) 1/2
(d) 0

A

Question. If the zeros of the polynomial x³ – 3x² + x +1 are p – q,p and p + q. Find the value of q.
(a) 1
(b) 0
(c) 2
(d) ±√2

D

Question. 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

B

Question. The zeroes of the quadratic polynomial x 2 + px + p, p ≠ 0 are
(a) both equal
(b) both cannot be positive
(c) both unequal
(d) both cannot be negative

B

Question. A quadratic polynomial has :
(a) at least 2 zeros
(b) exactly 2 zeros
(c) at most 2 zeros
(d) exactly 1 zero

C

Question. Which of the following Linear Graphs has no zero?

B

Question. If α, s are the roots of cx² – bx + a = 0 (c 0), then α + s is:
(a) -b/a
(b) b/a
(c) c/a
(d) b/c

D

Question. If a polynomial p(y) is divided by y + 2, then which of the following can be the remainder:
(a) y + 1
(b) 2y + 3
(c) 5
(d) y – 1

C

Question. If P(x) and D(r) are any two polynomials such that D(x) ≠ 0, there exists unique polynomial Q(x)and R(x) such that, P(x) = D(x). Q(x) + R(x) where :
(a) R(x) = 0 and deg R(x) > deg Q(x)
(b) R(x) = 0 or deg R(x) > deg D(x)
(c) deg R(x) < deg Q(x)
(d) R(x) = 0 or deg R(x) < deg D(x)

B

Question. When we divide x³ + 5x + 7 by x⁴ – 7x² – 6 then quotient and remainder are (respectively):
(a) 0,x³ + 5x + 7
(b) x, 2x + 3
(c) 1,x⁴ – 7x²-6
(d) x², 4x – 9

A

Question. The value of b, for which 2x³ + 9x² – x – b is exactly divisible by 2x + 3 is:
(a) -15
(b) 15
(c) 9
(d) – 9

B

Question. If α and s are two zeros of the polynomial p(x), then which of the following is a factor of p(x):
(a) (x – α)(x – s)
(b) (x + α) (x + s)
(c) k(x – α)
(d) k(x- s)

A

Question. The graph of a polynomial is as shown, find the polynomial
(a) k(x² – x – 6)
(b) k(x³ + x² + 6x)
(c) k(x³ – x² – 6x)
(d) k(x³ – 6x)

C

Question. If a polynomial p(x) is divided by b – ax; the remainder is the value of p(x) at x =
(a) a
(b) b/a
(c) -b/a
(d) a/b

B

Question. If α, s and v are the zeroes of the polynomial 2x³ – x² + 3x – 1, find the value of => (as + sv + va +asv )²
(a) 3/2
(b) 5/2
(c) 1/2
(d) 4

D

Question. If a and ß are the zeroes of the polynomial 5x 2 – 7x + 2, then sum of their reciprocals is:
(a) 14/25
(b) 7/5
(c) 2/5
(d) 7/2

D

Question. If 2 ± √3 are the two zeros of a polynomial then the following is a factor:
(a) x² – 4x + 1
(b) x² + 4x – 1
(c) 4x² + x – 1
(d) 4x² – x + 1

A

Question. Let, α, s, v be the zeroes of x³ + 4x² + x- 6 such that product of two of the zeroes is 6. Find thethird zero.
(a) 6
(b) 2
(c) 4
(d) 1

A

Question. Given that one of the zeroes of the polynomial ax³ + bx² + cx + d is zero, then the product of the other two zeroes is:
(a) -c/a
(b) c/a
(c) 0
(d) -b/a

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

B

Question. If the zeroes of the quadratic polynomial Ax 2 + Bx + C, C # 0 are equal, then
(a) A and B have the same sign
(b) A and C have the same sign
(c) B and C have the same sign
(d) A and C have opposite signs

B

Question. The number of polynomials having zeroes as 4 and 7 is
(a) 2
(b) 3
(c) 4
(d) more than 4

D

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) b – a + 1
(b) b – a – 1
(c) a – b + 1
(d) a – b – 1

A

Question. The number of zeros of a cubic polynomial is
(a) 3
(b) at least 3
(c) 2
(d) at most 3

D

Question. If a, s are the zeroes of x² – 8x + λ, such that α – s = 2, then X =
(a) 8
(b) 22
(c) 60
(d) 15

D

Question. Find the quadratic polynomial whose zeros are 2 and -6
(a) x 2 + 4x + 12
(b) x 2 – 4x – 12
(c) x 2 + 4x – 12
(d) x 2 – 4x + 12

C

Question. Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time and theproduct of its zeros as -2, +5, -3, respectively.
(a) 2x³ + 5x² + x + 3
(b) 4x³ + 5x² – 3x + 7
(c) x³ + 2x² + 5x + 3
(d) 2x³ + 5x² + 3x + 1

C

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

A

Question. Write a polynomial with zeros 1, – 1 and 1.
(a) x³ + x² + x + 1
(b) x³ – x² + x + 1
(c) x³ – x² – x – 1
(d) x³ – x² – x + 1

D

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

D

Question. The number of polynomials having zeroes – 1 and – 5 is :
(a) 2
(b) 3
(c) 1
(d) More than 3

D

Question. Sum and the product of zeroes of the polynomial x 2 +7x +10 is
(a) 10/7 and -10/7
(b) 7/10 and -7/10
(c) -7 and 10
(d) 7 and -10

C

Question. The zeroes of the quadratic polynomial 3×2 – 48 are
(a) both negative
(b) one positive and one negative
(c) both positive
(d) both equal

B

Question. If x = 2 and x = 3 are zeros of the quadratic polynomial x 2 + ax + b, the values of a and brespectively are :
(a) 5, 6
(b) – 5, – 6
(c) – 5, 6
(d) 5, – 6

C

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 unequal
(d) are always equal

A

Question. The sum and product of the zeroes of the polynomial x 2 -6x+8 are respectively
(a) -3/2 and – 1
(b) 6 and 8
(c) -3/2 and 1
(d) 3/2 and 1

B

Question. The number of polynomials having zeroes as -2 and 5 is
(a) 1
(b) 2
(c) 3
(d) more than 3

D

Question. The graph of the polynomial f(x) = 2x – 5 intersects the x – axis at
(a) (5/2 , 0)
(b) (-5/2 , 0)
(c) (-5/2 ,5/2 )
(d) (5/2 , -5/2)

A

Question. The graph of y = p(x), where p(x) is a polynomial in variable x, is as follows:

The number of zeroes of p(x) is
(a) 2
(b) 5
(c) 6
(d) None of these

B

Question. If the zero of polynomials 3x2 – px + 2 and 4x2 – qx – 10 is 2, the value of 2p –3q is
(a) 3
(b) 5
(c) 7
(d) –5

B

Question. If the graph of a polynomial intersects the x-axis at exactly two points, is it necessarily a
(b) cubic polynomial
(c) linear polynomial
(d) None of these

A

Question. How many of the above ten (in question 12), are quadratic polynomials?
(a) 0
(b) 1
(c) 2
(d) 3

B

Question. What number should be added to the polynomial x2 – 5x + 4, so that 3 is the zero of the polynomial ?
(a) 0
(b) 1
(c) 2
(d) 3

C

Question. If 2 is a zero of the polynomial ax2 – 2x, then the value of ‘a’ is
(a) 3
(b) 1
(c) 2
(d) 5

B

Question. For what value of k, (– 4) is a zero of p(x) = x2 – x – (2k – 2)?
(a) 8
(b) 11
(c) 13
(d) 15

B

Question. A teacher asked 10 of his students to write a polynomial in one variable on a paper and then to handover the paper. The following were the answers given by the students:
2x + 3, 3x2 + 7x + 2, 4x3 + 3x2 + 2, x3 + √3x + 7, 7x + √7 , 5x3 – 7x + 2, 2x2 + 3 – 5/ x , 5x – 1/ 2 , ax3 + bx2 + cx + d, x + 1/ x .
How many of the above ten, are not polynomials?
(a) 1
(b) 2
(c) 3
(d) 4

A

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

D

Question. A solution of 2x2 + 5x – 3 = 0 is
(a) –3
(b) 3
(c) –5
(d) 5

A

Question. The graph of a polynomial is shown in figure, then the number of its zeroes is

(a) 3
(b) 1
(c) 2
(d) 4

A

Question. If 1 is a zero of polynomial p(x) = ax2 – 3(a – 1) – 1, then the value of a is
(a) 0
(b) 1
(c) 3
(d) None of these

B

Question. The value of p, for which (–4) is a zero of the polynomial x2 – 2x – (7p + 3) is
(a) 0
(b) 2
(c) 3
(d) None of these

C

Question. The zeroes of the polynomial p(y) = 5 √5y2 + 30y + 8 √5 are
(a) −3/ √5, −7/ √11
(b) −2/√5 ,− 4/√5
(c)  3/ √5 , 3/√11
(d) 2/ √5 , 4/√5

B

Question. The zeroes of the polynomial x2 – 3x – m(m + 3) are
(a) m, m + 3
(b) –m, m + 3
(c) m, –(m + 3)
(d) –m, –(m + 3)

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): x2 + 4x + 5 has two zeroes.
Reason (R): A quadratic polynomial can have at the most two zeroes.
2. Assertion (A): A quadratic polynomial whose zeroes are 5 + 2 and 5 – 2 is x2 – 10 x + 23.
Reason (R): If a and b are zeroes of the quadratic polynomial p(x), then p(x) = x2 – (α + β) x + αβ.

1. (D) ,2. (A)

### Fill in the blanks:

Question. If a is a zero of p(x), then ________ is a factor of p(x).

(x – α)

Question. Division Algorithm for polynomials states that, Dividend = _________ x _________ +Remainder.

Divisor × coefficient

Question. A quadratic equation can have ________ two roots, .

atmost

Question. If a polynomial p(x) does not touch _______ axis, then it has no zeroes.

X – axis

One Word Questions :

Question. What is the three roots of the polynomial (x + 4) (x² – 6x + 8).

(2, 4, –4)

Question. How many maximum number of zeros a quadratic polynomial can have?

Two

Question. If one of the zero of the polynomial P(x) = x² – 13x + 40 is 8, which is the other zero?

5

Question. Find the zeros of the polynomial whose graph is given below :–

x = 2, x = 4

Question. Which are the two zeros of the quadratic polynomial given in figure?

2, 2

Question. Find the value of a in the polynomial x² + ax – 30 if 5 is the zero of the given polynomial.

a = 1

Question. If f(x) = x² – 5x – 14, find the value of f(7).

0

Question. If f(x) = 3x² – 7x + 8, find f(–2)

34

Question. Find the number of zeros of the polynomial y = f(x) whose graph is given below.

2 zeros

Question. Find the zeros of the polynomial x² – 25 = 0. Also give the sum of zeros.

(5, –5), 0

Question. Which is the factor common in 6(x + 1)(x + 2) and 9(x³ + 1)?

3 (x + 1)

Question. Find the zeros of the polynomial x² – 15x – 34

(17, –2)

Question. For what value of x, both the polynomials x² – 3x + 2 and x² – 6x + 5 becomes zero?

x = 1

Question. How many zeros does the polynomial f(x) = (x – 1)(x + 1)(x – 2) have in all?

3

Question. Find all the zeros of the polynomial f(x) = (x – 3)(x² – 9x + 20).

3, 4, 5

Question. What is the value of f (- 3/2) where f (x) = 4x2 + 3x + 7/2 ?

8

Question. What is the quotient and remainder if x² – 8x + 15 is divided by (x – 3)?

quotient (x – 5), R = 0

Question. In the polynomial 3x² – 4x – 7, find the sum of two zeros of the polynomial.

4/3

Question. From the graph given below find the number of zeros of the polynomial y = f(x).

4 zeros

Question. What will be the remainder if f(x) = x³ + 4x² – 3x + 1 is divided by (x – 2)?

19

Question. (x – 1) is a factor of (x³ + ax² + bx – 11) and a – b = 6. Find a and b.

a = 8, b = 2

Question. Find sum and product of the zeros of the polynomial. 3x² – 14x + 11

14/3 , 11/3

Question. Two roots of the polynomial x³ + x² – 9x – 9 are 3 and –3. What is the third root?

(–1)

Question. If P(x) = x² + 5x + 2, what is the value of P(3) + P(2)?

42

Question. Find the common zero of (x² + 2x + 1), (x² – 1) and x³ + 1.