Please refer to MCQ Questions Chapter 2 Polynomials Class 10 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 10 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 10 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 2 Polynomials in Class 10 Mathematics provided below to get more marks in exams.

**Chapter 2 Polynomials MCQ Questions**

Please refer to the following **Chapter 2 Polynomials MCQ Questions Class 10 Mathematics** with solutions for all important topics in the chapter.

**MCQ Questions Answers for Chapter 2 Polynomials Class 10 Mathematics**

**Question. If α ≠ β and the difference between the roots of the polynomials x ^{2} + ax + b and x^{2} + bx + a is the same, then **

(a) a + b + 4 = 0

(b) a + b − 4 = 0

(c) a − b + 4 = 0

(d) a − b − 4 = 0

**Answer**

A

**Question. The value of ‘a’, for which one root of the quadratic polynomial (a ^{2} −5a + 3) x^{2} + (3a − 1) x + 2 is twice as large as the other, is **

(a) − 1/ 3

(b) 2 /3

(c) − 2 /3

(d) 1/ 3

**Answer**

B

**Question. If α ≠ β and α ^{2} = 5α − 3, β^{2} = 5β − 3, then the polynomial whose zeros are α/β and β/α is : **

(a) 3x

^{2}− 25x + 3

(b) x

^{2}− 5x + 3

(c) x

^{2}+ 5x − 3

(d) 3x

^{2 }− 19x + 3

**Answer**

D

**Question. The homogeneous function of the second degree in x and y having 2x − y as a factor, taking the value 2 when x = y = 1 and vanishing if x = −1, y = 1 is **

(a) 2x^{2} + xy − y^{2}

(b) 3x^{2} − 2xy + y^{2}

(c) x^{2} + xy − 2y^{2}

(d) None of these

**Answer**

A

**Question. The common quantity that must be added to each term of a ^{2} : b^{2} to make it equal to a : b is **

(a) ab

(b) a + b

(c) a − b

(d) a/ b

**Answer**

A

**Question. The factors of a ^{2}(b^{3} − c^{3}) + b^{2}(c^{3} − a^{3}) + c^{2}(a^{3} − b^{3})are **

(a) (a − b) (b − c) (c − a) (ab + bc + ca)

(b) (a + b) (b + c) (c + a) (ab + bc + ca)

(c) (a − b) (b − c) (c − a) (ab − bc − ca)

(d) None of these

**Answer**

A

**Question. If p,q are zeros of x ^{2} + px + q, then **

(a) p = 1

(b) p = 1 or 0

(c) p = − 2

(d) p = − 2 or 0

**Answer**

A

**Question. On simplifying (a + b) ^{3} + (a − b)^{3} + 6a(a^{2} − b^{2}) we get **

(a) 8a

^{2}

(b) 8a

^{2}b

(c) 8a

^{3}b

(d) 8a

^{3}

**Answer**

D

**Question. Factors of (42 − x − x ^{2}) are **

(a) (x − 7)(x − 6)

(b) (x + 7)(x − 6)

(c) (x + 7)(6 − x)

(d) (x + 7)(x + 6)

**Answer**

C

**Question. If a − b = 3, a + b + x = 2, then the value of (a − b)[x ^{3} − 2ax2 + a^{2}x − (a + b)b^{2}] is **

(a) 84

(b) 48

(c) 32

(d) 36

**Answer**

B

**Question. If abx ^{2} = (a − b)^{2}(x + 1), then the value of 1 + 4/x + 4 x^{2} is:- **

(a) (a − b/a +b)

^{2}

(b) (a+b/a −b)

^{2}

(c) (a/a+b)

^{2}

(d) (b/a+b)

^{2}

**Answer**

B

**Question. Let a,b be the zeros of the polynomial (x − a) (x − b) − c with c ≠ 0. Then the zeros of the polyno- mial (x − α) (x − β) + c are **

(a) a, c

(b) b, c

(c) a, b

(d) a + c, b + c

**Answer**

C

**Question. Factors of (x ^{2} +x/6 −1/6) are **

(a) 1/ 6 (2x+1)(3x+1)

(b) 1/ 6 (2x+1)(3x−1)

(c) 1/ 6 (2x−1)(3x−1)

(d) 1/ 6 (2x−1)(3x+1)

**Answer**

B

**Question. If the polynomial x ^{19} + x^{17} + x^{13} + x^{11} + x^{7} + x^{5} + x^{3} is divided by (x^{2} + 1), then the remainder is **

(a) 1

(b) x

^{2}+ 4

(c) −x

(d) x

**Answer**

C

**Question. If (x − 2) is a common factor of x ^{3} − 4x^{2} + ax + b and x^{3} − ax^{2} + bx + 8, then the values of a and b are respectively **

(a) 3 and 5

(b) 2 and −4

(c) 4 and 0

(d) 0 and 4

**Answer**

D

**Question. In method of factorization of an algebraic expression, Which of the following statements is false? **

(a) Taking out a common factor from two or more terms

(b) Taking out a common factor from a group of terms

(c) By using remainder theorem

(d) By using standard identities

**Answer**

C

**Question. Factors of (a + b) ^{3} − (a − b)^{3} are **

(a) 2ab(3a

^{2}+ b

^{2})

(b) ab(3a

^{2}+ b

^{2})

(c) 2b(3a

^{2}+ b

^{2})

(d) 3a

^{2}+ b

^{2}0

**Answer**

C

**Question. Value of x ^{3} +b^{3} +c^{3} −3abc/ab +bc + ca −c^{2 }−b^{2} −c^{2} , when a = −5, b = −6, c = 10 is **

(a) 1

(b) −1

(c) 2

(d) −2

**Answer**

A

**Question. If (x + y + z) = 1, xy + yz + zx = −1, xyz = −1, then the value of x ^{3} + y^{3} + z^{3} is **

(a) −1

(b) 1

(c) 2

(d) −2

**Answer**

B

**Question. If the polynomial 16×4 − 24x ^{3} + 41x^{2} − mx + 16 be a perfect square,then the value of “m” is **

(a) 12

(b) −12

(c) 24

(d) −24

**Answer**

C

**Question. The square root of x ^{2}/y^{2} + y2/4x^{2} −x/y +y/2x −3/4 is **

(a) x/y −1/2 −y/2x

(b) x/y +1/2 −y/2x

(c) x/y +1/2 +y/2x

(d) x/y −1/4 −y/2x

**Answer**

A

**Question. If (3 + √3) is one of the zeroes of the quadratic polynomial x ^{2} + mx + 6 then find the second zero. **

(a) -√3

(b) 3 – √3

(c) 3 + √3

(d) √3

(e) None of these

**Answer**

B

**Question. If m = a + 1 /a – 1 and n = a – 1/a + 1 , then m ^{2} + n^{2} – 3 mn, is equal to **

**Answer**

A

**Question. For a quadratic polynomial 2x ^{2} – 8x + b , sum of its roots is 4 and one of the roots is 4 +√2/2 , then the value of b is_____ **

(a) 3

(b) 6

(c) 7

(d) 8

(e) None of these

**Answer**

C

**Question. If the zeroes of the quadratic polynomial p(x) = ax ^{2} – (b^{2} – ac) x – bc are α & β , then **

(a) α= -b

^{2}/a and α = -c

^{2}/b

(b) α = a/b and β = b/c

(c) α = b/a and β = -c/b

(d) α = -a/b and β = c/b

(e) None of these

**Answer**

C

**Question. If α and α are zeroes of the quadratic polynomial p(x) = ax ^{2} – bx + c , then the value of α/β + β/α is . **

(a) b

^{2}+ ac/ac

(b) b

^{2}– ac/ac

(c) b

^{2}+ 2ac/ac

(d) c

^{2}+ 2ac/ac

(e) None of these

**Answer**

B

**Question. If the zeroes of the quadratic polynomial ax ^{2} – x – b are -3/1 and 5/3 , then **

(a) a = 15, b = 6

(b) a = 6, b = 15

(c) a = 12, b = 4

(d) a = 4, b = 12

(e) None of these

**Answer**

B

**Question. If p(x) = 25x ^{2} – 15x – a where α and β are the zeroes of the polynomial, also if it is given that α^{3} + β^{3} = 63/125 , then **

(a) a = 5

(b) roots are -1/5 and 4/5

(c) a = 3

(d) roots are 1/5 and -2/5

(e) None of these

**Answer**

B

**Question. Which one among the following statements is incorrect? **

(a) Graph of a linear polynomial is a straight line whereas the graph of a quadratic polynomial has one of the two shapes of parabola either open upwards ∪ or open downwards ∩.

(b) The shape of the parabola depends on the value of ‘a’ of the quadratic polynomial ax^{2} + bx + c .

(c) The zeroes of a quadratic polynomial ax^{2} + bx +c , a ≠ 0 are y coordinates of the points where the parabola y= ax^{2} + bx + c intersects the y-axis.

(d) A real number m is a zero of the polynomial p(x) if p (m) = 0

(e) None of these

**Answer**

C

**Question. If all the zeroes of the cubic polynomia x ^{3} + cx^{2} + dx + b are equal, then **

(a) cd = 9 b

(b) bd = 8 b

(c) cd = 6 b

(d) bd = 8 b

(e) None of these

**Answer**

A

**Question. If the LCM of p(x) and q(x) is a ^{9} – b^{9} then their HCF can be **

(a) (a – b)

(b) (a

^{2}+ b

^{2}+ ab)

(c) a

^{6}+ b

^{6}+ a

^{3}b

^{3}

(d) All the above

(e) None of these

**Answer**

D

**Question. If (x − 3) is the factor of 3x ^{3} − x^{2} + px + q then___ **

(a) p + q = 72

(b) 3p + q = 72

(c) 3p + q = −72

(d) q − 3p = 72

**Answer**

C

**Question. For what values of n, (x + y) is a factor of (x − y) ^{n}. **

(a) for all values of n

(b) 1

(c) only for odd numbers

(d) none of these

**Answer**

D

**Question. If the zeros of the polynomial ax ^{2} + bx + c be in the ratio m : n, then **

(a) b

^{2}mn = (m2 + n

^{2}) ac

(b) (m + n)

^{2}ac = b2 mn

(c) b

^{2}(m

^{2}+ n

^{2}) = mnac

(d) None of these

**Answer**

B

**Question. A homogeneous expression of second degree in x & y is **

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

(b) ax^{2} + bx + cy

(c) ax^{2} + bx + cy^{2}

(d) ax^{2} + bxy + cy^{2}

**Answer**

D

**Question. If the sum of the zeros of the polynomial x ^{2} + px + q is equal to the sum of their squares, then **

(a) p

^{2}− q

^{2}= 0

(b) p

^{2}+ q

^{2}= 2q

(c) p

^{2}+ p = 2q

(d) None of these

**Answer**

C

**Question. The G.C.D of x ^{2} − 3x + 2 and x^{2} − 4x + 4 is **

(a) x − 2

(b) (x − 2)(x − 1)

(c) (x − 2)2

(d) (x − 2)3(x − 1)

**Answer**

A

**Question. If h(x) = 2x ^{3} + (6a^{2 }− 10) x^{2} + (6a + 2) x − 14a − 2 is exactly divisible by x − 1 but not by x + 1, then the value of a is **

(a) 0

(b) −1

(c) 10

(d) 2

**Answer**

D

**Question. Given the polynomial is exactly divided by x + 1, and when it is divided by 3x − 1, the remainder is 4. The polynomial gives a remainder hx + k when divided by 3×2 + 2x − 1 then the values of h and k are **

(a) h = 2, k = 3

(b) h = 3, k = 3

(c) h = 3, k = 2

(d) None of these

**Answer**

B

**Question. The G.C.D. of two polynomials is (x − 1) and their L.C.M. is x6 − 1. If one of the polynomials is x ^{3} − 1, then the other polynomial is_____. **

(a) x

^{3}− 1

(b) x

^{4}− x

^{3}+ x − 1

(c) x

^{2 }− x + 1

(d) None of these

**Answer**

B

**Question. The L.C.M. of 2x and 8 is **

(a) 2x

(b) 4x

(c) 8x

(d) 16x

**Answer**

C

**Question. If x ^{2} + 1/ x^{2} = 38, then the value of x − 1/ x is **

(a) 6

(b) 4

(c) 0

(d) None

**Answer**

A

**Question. The simplest form of (2x + 3) ^{3} − (2x − 3)^{3} is **

(a) 54 + 72x

^{2}

(b) 72 + 54x

^{2}

(c) 54 + 54x

^{2}

(d) None of these

**Answer**

A

**Question. The simplest form of (p − q) ^{3} + (q − r)^{3} + (r − p)^{3} is **

(a) 4(p − q)(q − r)(r − p)

(b) 2 (p − q)(q − r)(r − p)

(c) (p − q)(q − r)(r − p)

(d) None of these

**Answer**

C

**Question. The square root of x ^{4} + 6x^{3} + 17x^{2} + 24x + 16 is **

(a) x

^{2}+ 3x + 4

(b) 2x

^{2}+ 3x + 4

(c) 3x

^{2}+ 3x + 4

(d) None of these

**Answer**

A

**Question. The square root of x4 − 2x ^{3} + 3x^{2} − 2x + 1 is **

(a) x

^{2}+ x + 1

(b) x

^{2}− x + 1

(c) x

^{2}+ x − 1

(d) x

^{2}− x − 1

**Answer**

B

**Question. If x + 1/ x = 5, then the value of x ^{3} + 1/x^{3} is **

(a) 110

(b) 90

(c) 80

(d) 50

**Answer**

A

**Question. If x ^{3} −(x + 1)^{2} = 2001 then the value of x is **

(a) 14

(b) 13

(c) 10

(d) None

**Answer**

B

**Question. The value of l for which one zero of 3x ^{2} − (1 + 4λ) x + λ^{2} + 2 may be one-third of the other is **

(a) 4

(b) 33/ 8

(c) 17/ 4

(d) 31/ 8

**Answer**

D

**Question. The factors of a ^{3}(b − c) + b^{3}(c − a) + c^{3}(a − b) are **

(a) (a + b + c) (a − b) (b − c) (c − a)

(b) − (a + b + c) (a − b) (b − c) (c − a)

(c) 2 (a + b + c) (a − b) (b − c) (c − a)

(d) − 2 (a + b + c) (a − b) (b − c) (c − a)

**Answer**

B

**Question. If the expressions ax ^{3} + 3x^{2} − 3 and 2x^{3}− 5x + a on dividing by x − 4 leave the same remainder, then the value of a is **

(a) 1

(b) 0

(c) 2

(d) −1

**Answer**

A

**Question. If the polynomial x6 + px ^{5} + qx^{4} − x^{2} − x − 3 is divisible by x^{4} − 1, then the value of p^{2} + q^{2} is **

(a) 1

(b) 5

(c) 10

(d) 13

**Answer**

C

**Question. The value of m if 2xm + x ^{3} − 3x^{2} − 26 leaves a remainder of 226 when it is divided by x − 2. **

(a) 0

(b) 7

(c) 10

(d) All of these

**Answer**

B

**Question. The expression Ax ^{3} + x^{2} + Bx + C leaves remainder of 21 4 when divided by 1 − 2x and 18 when divided by x. Given also the expression has a factor of (x − 2), the values of A, B and C are **

(a) A = 5, B = − 9, C = 3

(b) A = 27, B = − 18, C = 4

(c) A = 4, B = − 27, C = 18

(d) None of these

**Answer**

C

**Question. The remainder when f(x) = (x ^{4} − x^{3} + 2x − 3) g(x) is divided by x − 3, given that x − 3 is a factor of g(x) + 3, where g(x) is a polynomial is **

(a) 0

(b) −171

(c) 10

(d) 2

**Answer**

B

**Question. If x ^{3} − hx^{2} + kx − 9 has a factor of x^{2} + 3, then the values of h and k are **

(a) h = 3, k = 3

(b) h = 2, k = 2

(c) h = 2, k = 1

(d) None of these

**Answer**

A

**Question. The L.C.M. of 22x(x + 1) ^{2} and 36x^{2}(2x^{2} + 3x + 1) is **

(a) 2x(x + 1)

(b) 396x

^{2}(x + 1)

^{2}(2x + 1)

(c) 792x

^{3}(x + 1)

^{2}(2x

^{2}+ 3x + 1)

(d) None of these

**Answer**

B

**Question. If 3x ^{3} + 2x^{2 }− 3x + 4 = (Ax + B)(x − 1)(x + 2) + C(x − 1) + D for all values of x, then A + B + C + D is **

(a) 0

(b) 14

(c) 10

(d) All

**Answer**

B

**Question. The expression x ^{3} + gx^{2} + hx + k is divisible by both x and x − 2 but leaves a remainder of 24 when divided by x + 2 then the values of g, h and k are **

(a) g = 10, h = − 3, k = 0

(b) g = 3, h = − 10, k = 0

(c) g = 10, h = − 2, k = 3

(d) None of these

**Answer**

B

**Question. The L.C.M of x ^{3} − 8 and x^{2} − 5x + 6 is **

(a) x − 2

(b) x

^{2}+ 2x + 4

(c) (x − 2)(x

^{2}+ 2x + 4)

(d) (x −2)(x − 3)(x

^{2}+ 2x + 4)

**Answer**

D

**Question. The polynomial f(x) has roots of equations 3, −3, −k. Given that the coefficient of x ^{3} is 2, and that f(x) has a remainder of 8 when divided by x + 1, the value of k is **

(a) 1/2

(b) 1/4

(c) 1/5

(d) 2

**Answer**

A

**Question. The cubic polynomials whose zeros are 4, 3/ 2 and −2 is : **

(a) 2x^{3} + 7x^{2} + 10x − 24

(b) 2x^{3} + 7x^{2} − 10x − 24

(c) 2x^{3} − 7x^{2} − 10x + 24

(d) None of these

**Answer**

C

**Question. One of the factors of x ^{3} + 3x^{2} − x − 3 is **

(a) x + 1

(b) x + 2

(c) x − 2

(d) x − 3

**Answer**

A

**Question. If ax ^{2} + 2a^{2}x + b^{3} is divisible by x + a, then _____. **

(a) a = b

(b) a + b = 0

(c) a

^{2}− ab + b

^{2}= 0

(d) a

^{2}+ 2ab + b

^{2}= 0

**Answer**

A

**Question. If x ^{3} + 2x^{2} + ax + b is exactly divisible by (x + a) and (x − 1), then _____. **

(a) a = −2

(b) b = −1

(c) a = −1

(d) b = 1

**Answer**

C

**Question. The quadratic polynomial whose sum and product of zeroes is 7 and –5 is: **

(a) x^{2} – 7x + 5

(b) x^{2} + 7x – 5

(c) x^{2} – 7x – 5

(d) none of these

**Answer**

C

**Question. If α,β are the zeroes of f(x) = x ^{2} + x + 1, then 1/ α + 1/ β is : **

(a) 0

(b) 1

(c) –1

(d) none of these

**Answer**

C

**Question. The cubic equation with zeroes 2, 3 and 4 is : **

(a) x^{3} – 9x^{2} + 26 x– 24

(b) x^{3} + 9x^{2} – 26x – 24

(c) x^{3} – 9x^{2} – 26x + 24

(d) none of these

**Answer**

A

**Question. The value of p(x) = x ^{3} – 6x^{2} + 11x – 6 at x = 3 is : **

(a) –38

(b) 0

(c) 12

(d) none of these

**Answer**

B

**Question. The quotient when f(x) = x ^{3} – 6x^{2} + 11x – 6 is divided by x + 2 is : **

(a) x

^{2}+ 8x – 27

(b) x

^{2}– 8x + 27

(c) x

^{2}– 8x – 27

(d) none of these

**Answer**

B

**Question. The graph of y = x ^{2} – 2x– 8 cuts the x-axis at: **

(a) –2 and 4

(b) 2 and –4

(c) do not cut

(d) none of these

**Answer**

A

**Question. The sum of squares of zeroes of f(x) = x ^{2} – 8x + k is 40. the value of k is **

(a) –12

(b) 12

(c) 24

(d) none of these

**Answer**

B

**Very Short Answer and Question :**

**Question. What should be subtracted from the polynomial x ^{2} – 7x –12 so that x = –4 is a zero of the polynomial ? **

**Answer**

**56**

**Question. Write a polynomial whose zeroes are –3 and 2/ 3 . **

**Answer**

** 3x ^{2} + 7x − 6**

**Question. How many zeroes does the polynomial p(x) – x(x – 2)(x – 3) have in all ? **

**Answer**

**3**

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

**Answer**

**2**

**Question. Give an example of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and deg r(x) = 0. **

**Answer**

** p(x) = x ^{2} + 5x + 7, g(x) = x + 2, q(x) = x + 3, r(x) = 1**

**Question. Find a quadratic polynomial whose two roots are 3 – √5 and 3 +√5 . **

**Answer**

** x ^{2} – 6x + 4**

**Question. Write the sum and the product of the zeroes of the polynomial 3x ^{2} – 5x + 9. sum = 5 /3 , product =**

**Answer**

**3**

**Question. What is the value of ‘p’ in the polynomial f (x) – x ^{2} –11x – p if –4 is a zero of the polynomial ? **

**Answer**

**28**

**Question. Find a cubic polynomial whose three zeroes are 0, 3, –3. **

**Answer**

**x ^{3} – 9x**

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