MCQ Questions for Class 10 Polynomials

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 x² +7x + 12
(1) -2, -5
(2) -3, -4
(3) 2, 5
(4) 3, 4

Question. Find the zeroes of the polynomial x² – 17
(1) √17, – √17
(2) √3, – √3
(3) √19, – √19
(4) none of these

Question. Find a quadratic polynomial, the sum and product of whose zeroes are -7 and -2
(1) x² -7x -2
(2) x² -7 x + 2
(3) x² + 7x -2
(4) x² + 2x -7

Question. Find a cubic polynomial when the zeroes are 3, -1, 1/3
(1) 3x³ – 5x² – 11x -3
(2) 3x³ + 5x² + 11x -3
(3) 3x³ -5x² + 11x + 3
(4) none of these

Question. Find a quadratic polynomial, the sum and product of whose zeroes are -1/4, 1/4
(1) 4x² – x + 1
(2) 4x² + x – 1
(3) 4x² + x + 1
(4) none of these

Question. Find all the zeroes of 2x⁴ – 3x³ – 3x² + 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

Question. Find the quotient and remainder when the polynomial x⁴ – 3x² + 4x + 5 is divided by x² – x + 1
(1) x² + x – 3, 8
(2) x² – x + 3, 7
(3) x² – x -3, 4
(4) x² + 2x + 3, 6

Question. The quotient and remainder are x – 2 and -2x + 4 respectively. If the polynomial x³ – 3x² + x + 2
is divided by g(x). Find g(x)
(1) x² + x + 1
(2) x² – x – 1
(3) x² – x + 1
(4) none of these

Question. Find P and q, if the zeroes of the polynomial x³ – 3x² + 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

Question. Find a quadratic polynomial whose zeroes are 7 + √9 / 2 and 7 – √9 / 2
(1) x² – 7x + 10
(2) x² + 7x + 10
(3) x² – 7x – 10
(4) x² + 7x – 10

Question. If the quotient and remainder were 3y – 5 and 9y + 10, on dividing 3y³ + y² + 2y + 5 by g (y). Find g (y)
(1) y² – 2y + 1
(2) y² + 2y + 1
(3) y² -2y – 1
(4) 2y² – 2y – 1

Question. Obtain the zeroes of the quadratic polynomial pqx² + (q² – Pr) x – qr

Question. If two of the zeroes are 2+√3 and 2 – √3. Find the other zeroes of t4 – 6t³ – 26t² + 138t – 35
(1) 7 and 5
(2) 7 and – 5
(3) (-6, 7)
(4) (-5 and -7)

Question. If p and q are the zeroes of the quadratic polynomial 4x² – 1 = 0. Find the value of p² + q²
(1) 3/2
(2) 1/4
(3) 1/2
(4) 1

Question. Find the zeroes of the quadratic polynomial x² + 19 x + 90
(1) -9, -10
(2) 9, 10
(3) 4, 5
(4) -4, -5

Question. Find the sum and product of zeroes of the polynomial x² – 2√3x + 4√3
(1) -2√3, -4√3
(2) 2√3, 4√3
(3) -2√3, 4√3
(4) 2√3, -4√3

Question. Find the zeroes of the polynomial x² – 21
(1) √21, – √21
(2) -3, 3
(3) 2√21, – 2√21
(4) none of these

Question. Find the sum and product of the zeroes of polynomial x² – 51
(1) 0, 51
(2) 0, -51
(3) 2, 51
(4) -2, 51

Question. Find the sum and product of the zeroes of quadratic polynomial 19x² – 16x – 21

Question. If p and q are the zeroes of the polynomial x² – 5x – k. Such that p – q = 1, find the value of K
(1) 6
(2) 7
(3) 8
(4) 9

Question. Find the sum and product of the zeroes of cubic polynomial 2x³ – 5x² – 14x + 8.
(1) 5/2, 7, -4
(2) -5/2, 7, -4
(3) -5/2, -7, 4
(4) 5/2, -7, 4

Question. Find the zeroes of the polynomial 4x² – 4x + 1
(1) -1/2
(2) 1/2
(3) 1
(4) 1/4

Question. Find the quotient and remainder, when the polynomial x⁴ – 5x + 6 is divided by 2 – x²
(1) – x² + 2, 5x – 10
(2) -x² – 2, – 5x + 10
(3) x² + 2, 5x – 10
(4) x² -2, – 5x + 10

Question. Form a quadratic polynomial of which one zero is 6 -√5 and the sum of the zeroes is
(1) x² – 4x + 30
(2) x² + 4x – 31
(3) x² – 12x + 31
(4) none of these

Question. Find the value of a so that -2 is a root of 2x² – x + a = 0
(1) 10
(2) – 10
(3) 9
(4) -9

Question. If p and q are the zeroes of the quadratic polynomial 2x³ + 3x + 5. Find the value of 1/p + 1/q
(1) 3/5
(2) 5/3
(3) -3/5
(4) – 5/3

Question. Find the quadratic polynomial whose sum and product of its zeroes are √2 and respectively
(1) 3x² -3√2x + 1
(2) 3x² + 3√2x – 1
(3) 3x² – 3√2x – 1
(4) none of these

Question. If P and q are the zeroes of the quadratic polynomial x² + mx + n² + a, then the value of p² + q² + pq is
(1) 0
(2) a
(3) -a
(4) +m²

Question. If , are the zeroes of the equation ax² + bx + c = 0, them form the quadratic polynomial whose zeroes are 2 + 3 , 3 + 2β
(1) 1/a² (a²x²+5abx + 6b² + ac)
(2) a² x² + 5abx + 6b² + ac
(3) ax² + abx + 6b² + ac
(4) a² x² + abx + b² + ac

Question. If p and q are the zeroes of the polynomial x² + px + q = 0, then
(1) p = 1
(2) p = 1 or 0
(3) p = -2
(4) p = -2 or 0

Question. If α & β are the zeroes of the quadratic polynomial 3x² – 11x + 6 , then find the polynomial whose zeroes are (2α + β)
(1) k (x² – 5x + 270/9 ) , k is any non-zero real number
(2) k (x² – 11x + 260/9 ) , k is any non-zero real number
(3) k (3x² – 3x + 26) , k is any non-zero real number
(4) k(2x² – 5x + 27), k is any non-zero real number
(5) None of these

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

Question. If p and q are the of the polynomial bx² + cx + a , value of 1/p³ + 1/q³ .
(1) 3abc – c³/ab²
(2) 3abc – c³/ab²
(3) 3abc – c³/a²b
(4) 3abc – c³/a²b
(5) None of these

Question. If α , β & ϒ are the roots of the equation x³ – 4x² – 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

Question. What must be subtracted from 6x⁴ + 16x³ + 15x² – 8x + 9 , so that it is exactly divisible by 3x² + 5x – 2 ?
(1) -19x + 15
(2) 19x + 16 
(3) 13x + 19 
(4) 19x + 15 
(5) None of these

Question. If f(x) = 3x⁴ +6x³ – 2x² – 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

Question. If (px) = x³ – 10x² + 31x – 30 and q(x) = x³ – 12x² + 41x – 42 , then find the LCM of the polynomials p(x) and q(x).
(1) x⁴ – 17x³ + 101x² – 247x + 210
(2) x³ – 36x² + 90x + 105
(3) x4 + 18x³ – 95x² + 234x – 119
(4) x³ – 18x² + 108x + 114
(5) None of these

Question. If the zeroes of the polynomial 6x² + 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

Question. What should be added to 1/x² – 12x + 32 to get 1/x² – 11x + 30 .
(1) 2x² – 25x + 96/(x – 6)(x – 5)(x – 4)(x – 8)
(2) 2x² – 25x – 66/(x – 6)(x – 5)(x – 4)(x – 8)
(3) 2x² – 25x + 66/(x – 6)(x – 5)(x – 4)(x – 8)
(4) 2/(x – 6)(x – 5)(x – 4)(x – 8)
(5) None of these

Question. If one zero of quadratic polynomial x² – x – k is the square of other, then find k
(1) 2 + √3
(2) 3 + √2
(3) 2 + √5
(4) 5 + √2

Question. If and are the zeroes of quadratic polynomial ax² + bx + c = 0, then find the value of

Question. If the product of zeroes of the quadratic polynomial mx² + 6x + (2m-1) is -1, then find the value of m
(1) 1/3
(2) 3
(3) -1/3
(4) – 3

Question. If the zeroes of the quadratic polynomial ax² + bx +c are of the form K + 1 / k and k + 2 / k + 1 , then find the value of (a + b + c)²
(1) b² + 4ac
(2) b² – 4ac
(3) a² + 4ac
(4) c² + 4ab

Question. If , are the zeroes of the quadratic polynomial ax² + bx +c , then form the quadratic polynomial whose zeroes are α + 1/β and  β + 1/α is
(1) 1/ac ((acx² + (a + c) bx + (a + c)²)
(2) abx² + (a + c) x + (a + b)²
(3) abx² + bx (a + c)²
(4) acx² + (a + b) (x+(a + b)²

Question. If the difference of the zeroes of the quadratic polynomial x² – bx + c be 1, then
(1) b² – 4c – 1 = 0
(1) b² – 4c = 0
(1) b² – 4c – 1 = 0
(1) b² + 4c – 1 = 0

Question. If , are the zeroes of the quadratic polynomial ax² + bx + c, then a/αβ+b + β/aα+b is
(1) 2 / a
(2) 2 / b
(3) 2 / c
(4) – 2 / a

Question. Find the zeroes of the polynomial x² + 2x + 1 = 0
(1) – 1, -1
(2) 1, 1
(3) – 1, 1
(4) -2, 1

Question. Find the zeroes of the quadratic polynomial 6x² – 7x – 3
(1) 3/2
(2) – 3/2 , 1/3
(3) – 3/2, – 1/3
(4) 3/2 , – 1/3

Question. Find the zeroes of the quadratic polynomial 5x² – 4 – 8x
(1) 2/5, -2
(2) -2/5, -2
(3) 2, -2/5
(4) 2/5, 2

Question. Find the quadratic polynomial whose zeroes are and respectively
(1) x² – 14x + 113
(2) x² – 14x – 113
(3) x² + 14x – 113
(4) None of these

Question. Find the sum and product of zeroes of the cubic polynomial p (x) = 5x³ – 10x² + 7x + 15
(1) 2, 7/5, -3
(2) -2, -7/5, 3
(3) 2, -7/5, 3
(4) -2, – 7/5, -3

Question. Find the remainder when y3 + 4y2 – 3y + 10 is divided by y + 4
(1) 22
(2) -22
(3) 21
(4) 20

Question. Find the quotient and remainder when 2t⁴ – 6t³ + 2t² – t + 2 is divided by t + 2
(1) 2t³ + 10t² -22t + 45, 91
(2) 2t² -20t + 45, 90
(3) 2t³ – 10t² + 22t – 45, 92
(4) 2t³ -22t + 45, 91

Question. Find the quotient and remainder when 4y³ -12y² + 14y -13 is divided by t – 1/2
(1) 4t² -10t + 9 , -17/2
(2) 4t² + 10t -9 , 17/2
(3) 4t² -10t – 9, 19/2
(4) 4t² + 4t + 5, 17/2

Question. If p and q are the zeroes of x² – 5x + 4 = 0, find the value of p²q + q²p
(1) 19
(2) 16
(3) 17
(4) 20

Question. Find the quotient and remainder when t⁴ + 1 is divided by t – 1
(1) t³ – t² – t – 1, 3
(2) t³ – t² + t – 1, 4
(3) t³ + t² + t + 1, 2
(4) t³ – t² – t + 1, 2

Question. Find the quotient and remainder when y⁴ + y² +1 is t³ divided by y² + y + 1
(1) y² – y + 1, 0
(2) y² + y + 1, 1
(3) y² – y – 1, 0
(4) y² + y -1, 2

Question. Form the quadratic polynomial in t when zeroes are 2+√5 and 2 -√5
(1) t² – 2t – 1
(2) t² – 4t – 1
(3) t² + t + 1
(4) t² – t – 1

Question. If and are the zeroes of x² – 6x + 4 = 0, Find the value of α²β² + α²β³
(1) 92
(2) 94
(3) 96
(4) 90

Question. The graph of a polynomial p(x) = ac² + 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

Question. If on dividing the polynomial f(x)=x³ – 4x² +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) x² + x + 1
(b) x² – x + 2
(c) 2x² + x + 1
(d) 2x² – x + 2
(e) None of these

Question. If α & are β 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

Question. If the zeroes of the polynomial x³ – 15x² + 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

Question. Find the value of a – b so that 8x⁴ + 14x³ – ax² + bx + 2 is exactly divisible by 4x² + 3x – 2
(a) 4
(b) 6
(c) 9
(d)-3
(e) None of these

Question. if m = a + 1/ a – 1 and n = a – 1 / a + 1 then m² + n² – 3mm is equal to

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

Question. if (x² + x – 1) is a factor of x⁴ + 9x³ + qx² – 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

One Word Questions :

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

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

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

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

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

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

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

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

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

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

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

Question. Reduce x² + 5x + 4 / x² + 2x + 1 to lowest terms.

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

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

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

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

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

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

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

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

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

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

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

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

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