Please refer to the **MCQ Questions for Class 10 Maths Polynomials **with Answers. The following Polynomials Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed MCQ Questions for Class 10 Maths with Answers for all chapters as per your NCERT Class 10 Mathematics book.

## Polynomials Class 10 MCQ Questions with Answers

Please see below Polynomials Class 10 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. Find the zeroes of the quadratic polynomial x ^{2} +7x + 12**

(1) -2, -5

(2) -3, -4

(3) 2, 5

(4) 3, 4

## **Answer**

2

**Question.** Find the zeroes of the polynomial x^{2} – 17

(1) √17, – √17

(2) √3, – √3

(3) √19, – √19

(4) none of these

## **Answer**

1

**Question.****Find a quadratic polynomial, the sum and product of whose zeroes are -7 and -2**

(1) x^{2 }-7x -2

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

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

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

## **Answer**

3

**Question.****Find a cubic polynomial when the zeroes are 3, -1, 1/3**

(1) 3x^{3} – 5x^{2} – 11x -3

(2) 3x^{3 }+ 5x^{2 }+ 11x -3

(3) 3x^{3} -5x^{2} + 11x + 3

(4) none of these

## Ans.

1

**Question.** Find a quadratic polynomial, the sum and product of whose zeroes are -1/4, 1/4

(1) 4x^{2} – x + 1

(2) 4x^{2} + x – 1

(3) 4x^{2} + x + 1

(4) none of these

## **Answer**

3

**Question.** Find all the zeroes of 2x^{4} – 3x^{3} – 3x^{2} + 6x – 2 if two of its zeroes √2 are and -√2

(1) √2,- √2, 1, -1/2

(2) √2, √2, -1, -1/2

(3) √2, – √2, 2, 1/2

(4) √2, – √2, 1/2×1

## **Answer**

4

**Question.** Find the quotient and remainder when the polynomial x^{4} – 3x^{2} + 4x + 5 is divided by x^{2} – x + 1

(1) x^{2} + x – 3, 8

(2) x^{2 }– x + 3, 7

(3) x^{2} – x -3, 4

(4) x^{2} + 2x + 3, 6

## **Answer**

1

**Question.** The quotient and remainder are x – 2 and -2x + 4 respectively. If the polynomial x^{3} – 3x^{2} + x + 2

is divided by g(x). Find g(x)

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

(2) x^{2 }– x – 1

(3) x^{2} – x + 1

(4) none of these

## **Answer**

3

**Question.** Find P and q, if the zeroes of the polynomial x^{3} – 3x^{2} + x + 1 are p-q, p, p + q

(1) p = +√2, q = 1

(2) p =√2, q = 2

(3) p = 2, q = √2

(4) p = 1, q = + √2

## **Answer**

4

**Question.** Find a quadratic polynomial whose zeroes are 7 + √9 / 2 and 7 – √9 / 2

(1) x^{2} – 7x + 10

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

(3) x^{2 }– 7x – 10

(4) x^{2} + 7x – 10

## **Answer**

1

**Question.** If the quotient and remainder were 3y – 5 and 9y + 10, on dividing 3y^{3} + y^{2} + 2y + 5 by g (y). Find g (y)

(1) y^{2} – 2y + 1

(2) y^{2} + 2y + 1

(3) y^{2} -2y – 1

(4) 2y^{2} – 2y – 1

## **Answer**

2

**Question.** Obtain the zeroes of the quadratic polynomial pqx^{2} + (q^{2} – Pr) x – qr

## **Answer**

1

**Question.** If two of the zeroes are 2+√3 and 2 – √3. Find the other zeroes of t4 – 6t^{3} – 26t^{2} + 138t – 35

(1) 7 and 5

(2) 7 and – 5

(3) (-6, 7)

(4) (-5 and -7)

## **Answer**

2

**Question.** If p and q are the zeroes of the quadratic polynomial 4x^{2} – 1 = 0. Find the value of p^{2} + q^{2}

(1) 3/2

(2) 1/4

(3) 1/2

(4) 1

## **Answer**

3

**Question.** Find the zeroes of the quadratic polynomial x^{2} + 19 x + 90

(1) -9, -10

(2) 9, 10

(3) 4, 5

(4) -4, -5

## **Answer**

1

**Question.** Find the sum and product of zeroes of the polynomial x^{2} – 2√3x + 4√3

(1) -2√3, -4√3

(2) 2√3, 4√3

(3) -2√3, 4√3

(4) 2√3, -4√3

## **Answer**

2

**Question.** Find the zeroes of the polynomial x^{2} – 21

(1) √21, – √21

(2) -3, 3

(3) 2√21, – 2√21

(4) none of these

## **Answer**

1

**Question.** Find the sum and product of the zeroes of polynomial x^{2} – 51

(1) 0, 51

(2) 0, -51

(3) 2, 51

(4) -2, 51

## **Answer**

2

**Question.** Find the sum and product of the zeroes of quadratic polynomial 19x^{2} – 16x – 21

## **Answer**

4

**Question.** If p and q are the zeroes of the polynomial x^{2} – 5x – k. Such that p – q = 1, find the value of K

(1) 6

(2) 7

(3) 8

(4) 9

## **Answer**

1

**Question.** Find the sum and product of the zeroes of cubic polynomial 2x^{3} – 5x^{2} – 14x + 8.

(1) 5/2, 7, -4

(2) -5/2, 7, -4

(3) -5/2, -7, 4

(4) 5/2, -7, 4

## **Answer**

1

**Question.** Find the zeroes of the polynomial 4x^{2} – 4x + 1

(1) -1/2

(2) 1/2

(3) 1

(4) 1/4

## **Answer**

2

**Question.** Find the quotient and remainder, when the polynomial x^{4} – 5x + 6 is divided by 2 – x^{2}

(1) – x^{2} + 2, 5x – 10

(2) -x^{2} – 2, – 5x + 10

(3) x^{2} + 2, 5x – 10

(4) x^{2} -2, – 5x + 10

## **Answer**

2

**Question.** Form a quadratic polynomial of which one zero is 6 -√5 and the sum of the zeroes is

(1) x^{2} – 4x + 30

(2) x^{2} + 4x – 31

(3) x^{2} – 12x + 31

(4) none of these

## **Answer**

3

**Question.** Find the value of a so that -2 is a root of 2x^{2} – x + a = 0

(1) 10

(2) – 10

(3) 9

(4) -9

## **Answer**

2

**Question.** If p and q are the zeroes of the quadratic polynomial 2x^{3} + 3x + 5. Find the value of 1/p + 1/q

(1) 3/5

(2) 5/3

(3) -3/5

(4) – 5/3

## **Answer**

1

**Question.** Find the quadratic polynomial whose sum and product of its zeroes are √2 and respectively

(1) 3x^{2} -3√2x + 1

(2) 3x^{2} + 3√2x – 1

(3) 3x^{2} – 3√2x – 1

(4) none of these

## **Answer**

1

**Question.** If P and q are the zeroes of the quadratic polynomial x^{2} + mx + n^{2} + a, then the value of p^{2} + q^{2} + pq is

(1) 0

(2) a

(3) -a

(4) +m^{2}

## **Answer**

3

**Question.** If , are the zeroes of the equation ax^{2} + bx + c = 0, them form the quadratic polynomial whose zeroes are 2 + 3 , 3 + 2β

(1) 1/a^{2} (a^{2}x^{2}+5abx + 6b^{2} + ac)

(2) a^{2 }x^{2} + 5abx + 6b^{2 }+ ac

(3) ax^{2 }+ abx + 6b^{2 }+ ac

(4) a^{2} x^{2 }+ abx + b^{2} + ac

## **Answer**

1

**Question.** If p and q are the zeroes of the polynomial x

^{2}+ px + q = 0, then

(1) p = 1

(2) p = 1 or 0

(3) p = -2

(4) p = -2 or 0

## **Answer**

2

**Question. If α & β are the zeroes of the quadratic polynomial 3x ^{2} – 11x + 6 , then find the polynomial whose zeroes are (2α + β) **

(1) k (x

^{2}– 5x + 270/9 ) , k is any non-zero real number

(2) k (x

^{2}– 11x + 260/9 ) , k is any non-zero real number

(3) k (3x

^{2}– 3x + 26) , k is any non-zero real number

(4) k(2x

^{2}– 5x + 27), k is any non-zero real number

(5) None of these

**Answer**

B

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

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

(1) 1

(2) 2

(3) 3

(4) 4

(5) None of these

**Answer**

D

**Question. If p and q are the of the polynomial bx ^{2} + cx + a , value of 1/p^{3} + 1/q^{3} . **

(1) 3abc – c

^{3}/ab

^{2}

(2) 3abc – c

^{3}/ab

^{2}

(3) 3abc – c

^{3}/a

^{2}b

(4) 3abc – c

^{3}/a

^{2}b

(5) None of these

**Answer**

E

**Question. If α , β & ϒ are the roots of the equation x ^{3} – 4x^{2} – 53x + 168 then the relation between their roots is _______ **

(1) 3α + β = 2ϒ

(2) 3α + 4β = 4ϒ

(3) 3α + β = 4ϒ

(4) α + 2β = ϒ

(5) None of these

**Answer**

C

**Question. What must be subtracted from 6x ^{4} + 16x^{3} + 15x^{2} – 8x + 9 , so that it is exactly divisible by 3x^{2} + 5x – 2 ? **

(1) -19x + 15

(2) 19x + 16

(3) 13x + 19

(4) 19x + 15

(5) None of these

**Answer**

A

**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 _______ **

(1) √3/5 , – √3/5

(2) √2/5 , – √2/5

(3) √5/3 , -√5/3

(4) √5/4 , – √5/4

(5) None of these

**Answer**

C

**Question. If (px) = x ^{3} – 10x^{2} + 31x – 30 and q(x) = x^{3} – 12x^{2} + 41x – 42 , then find the LCM of the polynomials p(x) and q(x). **

(1) x

^{4}– 17x

^{3}+ 101x

^{2}– 247x + 210

(2) x

^{3}– 36x

^{2}+ 90x + 105

(3) x4 + 18x

^{3}– 95x

^{2}+ 234x – 119

(4) x

^{3}– 18x

^{2}+ 108x + 114

(5) None of these

**Answer**

A

**Question. If the zeroes of the polynomial 6x ^{2} + 7√3x – 15 = 0 are α & β , then **

(1) α = -√3/2 & β = 5√3/3

(2) α = -√3 & β = 5√3

(3) α = √3/2 -5√3/3

(4) α = 5√3 & β = -√3

(5) None of these

**Answer**

C

**Question. What should be added to 1/x ^{2} – 12x + 32 to get 1/x^{2} – 11x + 30 . **

(1) 2x

^{2}– 25x + 96/(x – 6)(x – 5)(x – 4)(x – 8)

(2) 2x

^{2}– 25x – 66/(x – 6)(x – 5)(x – 4)(x – 8)

(3) 2x

^{2}– 25x + 66/(x – 6)(x – 5)(x – 4)(x – 8)

(4) 2/(x – 6)(x – 5)(x – 4)(x – 8)

(5) None of these

**Answer**

C

** Question.** If one zero of quadratic polynomial x

^{2}– x – k is the square of other, then find k

(1) 2 + √3

(2) 3 + √2

(3) 2 + √5

(4) 5 + √2

## **Answer**

3

** Question.** If and are the zeroes of quadratic polynomial ax

^{2}+ bx + c = 0, then find the value of

## **Answer**

1

** Question.** If the product of zeroes of the quadratic polynomial mx

^{2}+ 6x + (2m-1) is -1, then find the value of m

(1) 1/3

(2) 3

(3) -1/3

(4) – 3

## **Answer**

1

** Question.** If the zeroes of the quadratic polynomial ax

^{2}+ bx +c are of the form K + 1 / k and k + 2 / k + 1 , then find the value of (a + b + c)

^{2}

(1) b

^{2}+ 4ac

(2) b

^{2 }– 4ac

(3) a

^{2}+ 4ac

(4) c

^{2}+ 4ab

## **Answer**

2

**Question. If , are the zeroes of the quadratic polynomial ax^{2} + bx +c , then form the quadratic polynomial whose zeroes are α + 1/β and β + 1/α is**(1) 1/ac ((acx

^{2 }+ (a + c) bx + (a + c)

^{2})

(2) abx

^{2}+ (a + c) x + (a + b)

^{2}

(3) abx

^{2}+ bx (a + c)

^{2}

(4) acx

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

^{2}

## **Answer**

1

** Question.** If the difference of the zeroes of the quadratic polynomial x

^{2 }– bx + c be 1, then

(1) b

^{2}– 4c – 1 = 0

(1) b

^{2 }– 4c = 0

(1) b

^{2 }– 4c – 1 = 0

(1) b

^{2}+ 4c – 1 = 0

## **Answer**

1

**Question. If , are the zeroes of the quadratic polynomial ax^{2 }+ bx + c, then a/αβ+b + β/aα+b is**(1) 2 / a

(2) 2 / b

(3) 2 / c

(4) – 2 / a

## **Answer**

4

** Question.** Find the zeroes of the polynomial x

^{2}+ 2x + 1 = 0

(1) – 1, -1

(2) 1, 1

(3) – 1, 1

(4) -2, 1

## **Answer**

1

** Question.** Find the zeroes of the quadratic polynomial 6x

^{2}– 7x – 3

(1) 3/2

(2) – 3/2 , 1/3

(3) – 3/2, – 1/3

(4) 3/2 , – 1/3

## **Answer**

4

** Question.** Find the zeroes of the quadratic polynomial 5x

^{2}– 4 – 8x

(1) 2/5, -2

(2) -2/5, -2

(3) 2, -2/5

(4) 2/5, 2

## **Answer**

3

** Question.** Find the quadratic polynomial whose zeroes are and respectively

(1) x

^{2}– 14x + 113

(2) x

^{2}– 14x – 113

(3) x

^{2}+ 14x – 113

(4) None of these

## **Answer**

2

**Question.****Find the sum and product of zeroes of the cubic polynomial p (x) = 5x ^{3} – 10x^{2} + 7x + 15**

(1) 2, 7/5, -3

(2) -2, -7/5, 3

(3) 2, -7/5, 3

(4) -2, – 7/5, -3

## **Answer**

1

**Question.****Find the remainder when y3 + 4y2 – 3y + 10 is divided by y + 4**

(1) 22

(2) -22

(3) 21

(4) 20

## **Answer**

1

**Question.****Find the quotient and remainder when 2t ^{4} – 6t^{3} + 2t^{2} – t + 2 is divided by t + 2**

(1) 2t

^{3}+ 10t

^{2}-22t + 45, 91

(2) 2t

^{2}-20t + 45, 90

(3) 2t

^{3}– 10t

^{2}+ 22t – 45, 92

(4) 2t

^{3}-22t + 45, 91

## **Answer**

3

**Question.**** Find the quotient and remainder when 4y ^{3} -12y^{2} + 14y -13 is divided by t – 1/2**

(1) 4t

^{2}-10t + 9 , -17/2

(2) 4t

^{2}+ 10t -9 , 17/2

(3) 4t

^{2}-10t – 9, 19/2

(4) 4t

^{2}+ 4t + 5, 17/2

## **Answer**

1

**Question.****If p and q are the zeroes of x ^{2} – 5x + 4 = 0, find the value of p^{2}q + q^{2}p**

(1) 19

(2) 16

(3) 17

(4) 20

## **Answer**

4

** Question.** Find the quotient and remainder when t

^{4}+ 1 is divided by t – 1

(1) t

^{3}– t

^{2}– t – 1, 3

(2) t

^{3}– t

^{2}+ t – 1, 4

(3) t

^{3}+ t

^{2}+ t + 1, 2

(4) t

^{3}– t

^{2}– t + 1, 2

## **Answer**

3

** Question.** Find the quotient and remainder when y

^{4}+ y

^{2}+1 is t

^{3}divided by y

^{2}+ y + 1

(1) y

^{2}– y + 1, 0

(2) y

^{2 }+ y + 1, 1

(3) y

^{2}– y – 1, 0

(4) y

^{2}+ y -1, 2

## **Answer**

1

** Question.** Form the quadratic polynomial in t when zeroes are 2+√5 and 2 -√5

(1) t

^{2}– 2t – 1

(2) t

^{2}– 4t – 1

(3) t

^{2}+ t + 1

(4) t

^{2}– t – 1

## **Answer**

2

**Question. If and are the zeroes of x^{2} – 6x + 4 = 0, Find the value of α^{2}β^{2} + α^{2}β^{3}**(1) 92

(2) 94

(3) 96

(4) 90

## **Answer**

3

**Question.****The graph of a polynomial p(x) = ac ^{2} + bx + c is shown below:**

**Based on the above graph which one is correct?**

(a) a > 0, b > 0, c > 0

(b) a < 0, b < 0, c > 0

(c) a < 0, b < 0, c < 0

(d) a > 0, b < 0, c > 0

(e) None of these

## **Answer**

D

**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

## Ans.

B

**Question.** If α & are β the zeroes of the polynomial x^{2} + 6x – k such that 2β + α = 11 then k is equal to

(a) 18

(b) -23

(c) 391

(d) – 391

(e) None of these

## **Answer**

C

**Question.****If the zeroes of the polynomial x ^{3} – 15x^{2} + 66x – 80 are α,β & y and it is also given that 2β + α + y then**

(a) α = 4

(b) y = 3

(c) y = 7

(d) α = 2

(e) None of these

## **Answer**

D

**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 m = a + 1/ a – 1 and n = a – 1 / a + 1 then m^{2} + n^{2} – 3mm is equal to

## **Answer**

A

**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**

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

**One Word Questions :**

**Question. What is the product of zeros of the polynomial x² – 11x + 30?**

**Answer**

30

**Question. Find both the zeros of the polynomial 2x² – 3x – 14**

**Answer**

( 7/2 , -2)

**Question. Which factor is common in x² + 8x + 15 and x² + 3x – 10?**

**Answer**

(x + 5)

**Question. Which of the numbers 3, 2, –2, 1 are zeros of the polynomial x² – 4?**

**Answer**

(2, –2)

**Question. What is the sum and product of 3 roots of the cubic polynomial x³ – 7x + 6?**

**Answer**

(0, –6)

**Question. Which factor is common in x² – 1, x4 – 1 and (x – 1)²?**

**Answer**

(x – 1)

**Question. Find the quadratic polynomial whose two roots (zeros) are 3+ √5 and 3 – √5 .**

**Answer**

x² – 6x + 4

**Question. Find the polynomial whose roots are 2 √3 and 3 √3.**

**Answer**

x² – 5 √3+18

**Question. For what value of k, (x = –4) is a zero of the polynomial 2x² + kx – 12?**

**Answer**

k = 5

**Question. Find the quotient when x² – 7x + 12 is divided by (x – 3).**

**Answer**

(x – 4)

**Question. What is the quotient if x³ – 1 is divided by x² + x + 1?**

**Answer**

(x – 1)

**Question. Reduce x ^{2} + 5x + 4 / x^{2} + 2x + 1 to lowest terms.**

**Answer**

x + 4 / x + 1

**Question. If (x + 2) is a factor of x² + ax + 2b and a + b = 4 then what is the value of a and b?**

**Answer**

a = 3, b = 1

**Question. For what value of x both the polynomials 3x² + 8x + 4 and x² – x – 6 becomes zero?**

**Answer**

x = –2

**Question. What should be added to the polynomial x² – 5x + 4, so that 3 is the zero of the polynomial?**

**Answer**

2

**Question. Find the cubic polynomial whose three zeros are 0, 4, –4.**

**Answer**

x³ – 16x

**Question. Find the polynomial whose zeros are √2 and – √2.**

**Answer**

x² – 2

**Question. Complete the following :–****Dividend = Divisor x __________ + __________**

**Answer**

Quotient, Remainder

**Question. Which quadratic polynomial have its zeros as 1/4 and 3/4 ?**

**Answer**

1/16 (16x² – 16x + 3)

**Question. For what value of a, (x = 6) is a zero of the polynomial x² – ax – 6?**

**Answer**

a = 5

**Question. What is the value of ‘k’ in the polynomial P(x) = x² + 11x + k if –4 is a zero of the polymnomial?**

**Answer**

k = 28

**Question. What is the coefficient of x² in the polynomial P(x) = 3x³ 10(x – x²) – 5x² – 2 ?**

**Answer**

–15

**Question. Which quadratic polynomial have the sum and product of roots as –15 and 50?**

**Answer**

x² + 15x + 50

**Question. What should be subtracted from the polynomial x² – 16x + 30 so that x = 15 is a zero of the polynomial?**

**Answer**

15

**Question. Find the value of the polynomial P(x) when x = 3.****P(x) = x² – 4x + 7**

**Answer**

4