MCQ Questions Chapter 2 Polynomials Class 10 Mathematics

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 x² + ax + b and x² + 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

Question. The value of ‘a’, for which one root of the quadratic polynomial (a² −5a + 3) x² + (3a − 1) x + 2 is twice as large as the other, is
(a) − 1/ 3
(b) 2 /3
(c) − 2 /3
(d) 1/ 3

Question. If α ≠ β and α² = 5α − 3, β² = 5β − 3, then the polynomial whose zeros are α/β and β/α is :
(a) 3x² − 25x + 3
(b) x² − 5x + 3
(c) x² + 5x − 3
(d) 3x² − 19x + 3

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) 2x² + xy − y²
(b) 3x² − 2xy + y²
(c) x² + xy − 2y²
(d) None of these

Question. The common quantity that must be added to each term of a² : b² to make it equal to a : b is
(a) ab
(b) a + b
(c) a − b
(d) a/ b

Question. The factors of a²(b³ − c³) + b²(c³ − a³) + c²(a³ − b³)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

Question. If p,q are zeros of x² + px + q, then
(a) p = 1
(b) p = 1 or 0
(c) p = − 2
(d) p = − 2 or 0

Question. On simplifying (a + b)³ + (a − b)³ + 6a(a² − b²) we get
(a) 8a²
(b) 8a²b
(c) 8a³b
(d) 8a³

Question. Factors of (42 − x − x²) are
(a) (x − 7)(x − 6)
(b) (x + 7)(x − 6)
(c) (x + 7)(6 − x)
(d) (x + 7)(x + 6)

Question. If a − b = 3, a + b + x = 2, then the value of (a − b)[x³ − 2ax2 + a²x − (a + b)b²] is
(a) 84
(b) 48
(c) 32
(d) 36

Question. If abx² = (a − b)²(x + 1), then the value of 1 + 4/x + 4 x² is:-
(a) (a − b/a +b)²
(b) (a+b/a −b)²
(c) (a/a+b)²
(d) (b/a+b)²

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

Question. Factors of (x² +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)

Question. If the polynomial x¹⁹ + x¹⁷ + x¹³ + x¹¹ + x⁷ + x⁵ + x³ is divided by (x² + 1), then the remainder is
(a) 1
(b) x² + 4
(c) −x
(d) x

Question. If (x − 2) is a common factor of x³ − 4x² + ax + b and x³ − ax² + 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

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

Question. Factors of (a + b)³ − (a − b)³ are
(a) 2ab(3a² + b²)
(b) ab(3a² + b²)
(c) 2b(3a² + b²)
(d) 3a² + b²0

Question. Value of x³ +b³ +c³ −3abc/ab +bc + ca −c² −b² −c² , when a = −5, b = −6, c = 10 is
(a) 1
(b) −1
(c) 2
(d) −2

Question. If (x + y + z) = 1, xy + yz + zx = −1, xyz = −1, then the value of x³ + y³ + z³ is
(a) −1
(b) 1
(c) 2
(d) −2

Question. If the polynomial 16×4 − 24x³ + 41x² − mx + 16 be a perfect square,then the value of “m” is
(a) 12
(b) −12
(c) 24
(d) −24

Question. The square root of x²/y² + y2/4x² −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

Question. If (3 + √3) is one of the zeroes of the quadratic polynomial x² + mx + 6 then find the second zero.
(a) -√3
(b) 3 – √3
(c) 3 + √3
(d) √3
(e) None of these

Question. If m = a + 1 /a – 1 and n = a – 1/a + 1 , then m² + n² – 3 mn, is equal to

Question. For a quadratic polynomial 2x² – 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

Question. If the zeroes of the quadratic polynomial p(x) = ax² – (b² – ac) x – bc are α & β , then
(a) α= -b²/a and α = -c²/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

Question. If α and α are zeroes of the quadratic polynomial p(x) = ax² – bx + c , then the value of α/β + β/α is .
(a) b² + ac/ac
(b) b² – ac/ac
(c) b² + 2ac/ac
(d) c² + 2ac/ac
(e) None of these

Question. If the zeroes of the quadratic polynomial ax² – 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

Question. If p(x) = 25x² – 15x – a where α and β are the zeroes of the polynomial, also if it is given that α³ + β³ = 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

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 ax² + bx + c .
(c) The zeroes of a quadratic polynomial ax² + bx +c , a ≠ 0 are y coordinates of the points where the parabola y= ax² + 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

Question. If all the zeroes of the cubic polynomia x³ + cx² + 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

Question. If the LCM of p(x) and q(x) is a⁹ – b⁹ then their HCF can be
(a) (a – b)
(b) (a² + b² + ab)
(c) a⁶ + b⁶ + a³ b³
(d) All the above
(e) None of these

Question. If (x − 3) is the factor of 3x³ − x² + px + q then___
(a) p + q = 72
(b) 3p + q = 72
(c) 3p + q = −72
(d) q − 3p = 72

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

Question. If the zeros of the polynomial ax² + bx + c be in the ratio m : n, then
(a) b² mn = (m2 + n²) ac
(b) (m + n)² ac = b2 mn
(c) b² (m² + n²) = mnac
(d) None of these

Question. A homogeneous expression of second degree in x & y is
(a) ax² + bx + c
(b) ax² + bx + cy
(c) ax² + bx + cy²
(d) ax² + bxy + cy²

Question. If the sum of the zeros of the polynomial x² + px + q is equal to the sum of their squares, then
(a) p² − q² = 0
(b) p² + q² = 2q
(c) p² + p = 2q
(d) None of these

Question. The G.C.D of x² − 3x + 2 and x² − 4x + 4 is
(a) x − 2
(b) (x − 2)(x − 1)
(c) (x − 2)2
(d) (x − 2)3(x − 1)

Question. If h(x) = 2x³ + (6a² − 10) x² + (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

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

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 x³ − 1, then the other polynomial is_____.
(a) x³ − 1
(b) x⁴ − x³ + x − 1
(c) x² − x + 1
(d) None of these

Question. The L.C.M. of 2x and 8 is
(a) 2x
(b) 4x
(c) 8x
(d) 16x

Question. If x² + 1/ x² = 38, then the value of x − 1/ x is
(a) 6
(b) 4
(c) 0
(d) None

Question. The simplest form of (2x + 3)³ − (2x − 3)³ is
(a) 54 + 72x²
(b) 72 + 54x²
(c) 54 + 54x²
(d) None of these

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

Question. The square root of x⁴ + 6x³ + 17x² + 24x + 16 is
(a) x² + 3x + 4
(b) 2x² + 3x + 4
(c) 3x² + 3x + 4
(d) None of these

Question. The square root of x4 − 2x³ + 3x² − 2x + 1 is
(a) x² + x + 1
(b) x² − x + 1
(c) x² + x − 1
(d) x² − x − 1

Question. If x + 1/ x = 5, then the value of x³ + 1/x³ is
(a) 110
(b) 90
(c) 80
(d) 50

Question. If x³ −(x + 1)² = 2001 then the value of x is
(a) 14
(b) 13
(c) 10
(d) None

Question. The value of l for which one zero of 3x² − (1 + 4λ) x + λ² + 2 may be one-third of the other is
(a) 4
(b) 33/ 8
(c) 17/ 4
(d) 31/ 8

Question. The factors of a³(b − c) + b³(c − a) + c³(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)

Question. If the expressions ax³ + 3x² − 3 and 2x³− 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

Question. If the polynomial x6 + px⁵ + qx⁴ − x² − x − 3 is divisible by x⁴ − 1, then the value of p² + q² is
(a) 1
(b) 5
(c) 10
(d) 13

Question. The value of m if 2xm + x³ − 3x² − 26 leaves a remainder of 226 when it is divided by x − 2.
(a) 0
(b) 7
(c) 10
(d) All of these

Question. The expression Ax³ + x² + 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

Question. The remainder when f(x) = (x⁴ − x³ + 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

Question. If x³ − hx² + kx − 9 has a factor of x² + 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

Question. The L.C.M. of 22x(x + 1)² and 36x²(2x² + 3x + 1) is
(a) 2x(x + 1)
(b) 396x²(x + 1)²(2x + 1)
(c) 792x³(x + 1)² (2x² + 3x + 1)
(d) None of these

Question. If 3x³ + 2x² − 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

Question. The expression x³ + gx² + 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

Question. The L.C.M of x³ − 8 and x² − 5x + 6 is
(a) x − 2
(b) x² + 2x + 4
(c) (x − 2)(x² + 2x + 4)
(d) (x −2)(x − 3)(x² + 2x + 4)

Question. The polynomial f(x) has roots of equations 3, −3, −k. Given that the coefficient of x³ 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

Question. The cubic polynomials whose zeros are 4, 3/ 2 and −2 is :
(a) 2x³ + 7x² + 10x − 24
(b) 2x³ + 7x² − 10x − 24
(c) 2x³ − 7x² − 10x + 24
(d) None of these

Question. One of the factors of x³ + 3x² − x − 3 is
(a) x + 1
(b) x + 2
(c) x − 2
(d) x − 3

Question. If ax² + 2a²x + b³ is divisible by x + a, then _____.
(a) a = b
(b) a + b = 0
(c) a² − ab + b² = 0
(d) a² + 2ab + b² = 0

Question. If x³ + 2x² + ax + b is exactly divisible by (x + a) and (x − 1), then _____.
(a) a = −2
(b) b = −1
(c) a = −1
(d) b = 1

Question. The quadratic polynomial whose sum and product of zeroes is 7 and –5 is:     
(a) x² – 7x + 5
(b) x² + 7x – 5
(c) x² – 7x – 5
(d) none of these

Question. If α,β are the zeroes of f(x) = x² + x + 1, then 1/ α + 1/ β  is :     
(a) 0
(b) 1
(c) –1
(d) none of these

Question. The cubic equation with zeroes 2, 3 and 4 is :     
(a) x³ – 9x² + 26 x– 24
(b) x³ + 9x² – 26x – 24
(c) x³ – 9x² – 26x + 24
(d) none of these

Question. The value of p(x) = x³ – 6x² + 11x – 6 at x = 3 is :       
(a) –38
(b) 0
(c) 12
(d) none of these

Question. The quotient when f(x) = x³ – 6x² + 11x – 6 is divided by x + 2 is :     
(a) x² + 8x – 27
(b) x² – 8x + 27
(c) x² – 8x – 27
(d) none of these

Question. The graph of y = x² – 2x– 8 cuts the x-axis at:   
(a) –2 and 4
(b) 2 and –4
(c) do not cut
(d) none of these

Question. The sum of squares of zeroes of f(x) = x² – 8x + k is 40. the value of k is   
(a) –12 
(b) 12
(c) 24
(d) none of these

Very Short Answer and Question :

Question. What should be subtracted from the polynomial x² – 7x –12 so that x = –4 is a zero of the polynomial ?   

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

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

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

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. 

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

Question. Write the sum and the product of the zeroes of the polynomial 3x² – 5x + 9.  sum = 5 /3 , product =

Question. What is the value of ‘p’ in the polynomial f (x) – x² –11x – p if –4 is a zero of the polynomial ?    

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

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