CBSE Class 10 Mathematics Polynomials MCQs Set E

Question. If 2 and 3 are the zeros of f(x) = 2x³ + mx² − 13x + n, then the values of m and n are respectively −
(a) −5, − 30
(b) −5, 30
(c) 5, 30
(d) 5, − 30

Answer: B

Question. If a,b are the zeros of the polynomial 6x² + 6px + p², then the polynomial whose zeros are (α + β)² and (α −β)² is −
(a) 3x² + 4p²x + p⁴
(b) 3x² + 4p²x − p⁴
(c) 3x² − 4p²x + p⁴
(d) None of the options

Answer: B

Question. ax⁴ + bx³ + cx² + dx + e is exactly divisible by x² − 1, when:
(a) a + b + c + e = 0
(b) a + c + e = 0
(c) a + b = 0
(d) a + c + e = b + d = 1

Answer: B

Question. If x + 1 is a factor of ax⁴ + bx³ + cx² + dx + e = 0 then ____
(a) a + c + e = b + d
(b) a + b = c + d
(c) a + b + c + d + e = 0
(d) a + c + b = d + e

Answer: A

Question. Consider f(x) = 8x⁴ − 2x² + 6x − 5 and a,b,g,d are it's zeros then α + β + γ + δ =
(a) 1/ 4
(b) − 1/ 4
(c) −3/2
(d) None of the options

Answer: D

Question. If (x − 3), (x −3) are factors of x³ − 4x² − 3x + 18; then the other factor is
(a) x + 2
(b) x + 3
(c) x − 2
(d) x + 6

Answer: A

Question. If α, β and γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d, then 1/α +1/β +1/γ =
(a) −b/ a
(b) c/ d
(c) −c/d
(d) −c / a

Answer: B

Question. If a, b and g are the zeros of the polynomial f(x) = ax³ − bx² + cx − d, then α² +β² + γ² =
(a) b² −ac/a²
(b) b² +2ac/b²
(c) b² −2ac/a
(d) b² −2ac/a²

Answer: D

Question. If α,β,γ are the zeros of the polynomial x³ − 3x + 11, then the polynomial whose zeros are (α+β), (β+γ) and (γ+α) is −
(a) x³ + 3x + 11
(b) x³ − 3x + 11
(c) x³ + 3x − 11
(d) x³ − 3x − 11

Answer: D

Question. If α,β,γ are such that α + β + γ = 2, α² + β² + γ² = 6, α³ + β³ + γ³ = 8, then α4 + β⁴ + γ⁴ is equal to
(a) 10
(b) 12
(c) 18
(d) None of the options

Answer: B

Question. The sum and product of zeroes of quadratic polynomial 3x² – 8x + 12 is :
(a) −8/3 , 4 
(b) 8/3 , 4 
(c) −8/3 , −4 
(d) none of the options

Answer: B

Question. The number of polynomials having zeroes as –2 and 5 is
(a) 1
(b) 2
(c) 10
(d) infinite

Answer: D

Question. The set of the zeroes of the polynomial x² – 25, their sum and product is
(a) 4, 3; 7; 12
(b) –3, 3; 0; –9
(c) 5, –5; 0; –25
(d) None of the options

Answer: B

Question. If the product of the zeroes of the polynomial ax² – 6x – 6 is 4, then value of a is
(a) 1/8
(b) – 1/4
(c) 5/3
(d) –3/2 

Answer: D

Question. If α,β are zeros of ax² + bx + c, ac ≠ 0, then zeros of cx² + bx + a are −
(a) − α − β
(b) α,1/ β
(c) β,1/ α
(d) 1/α,1 /β

Answer: D

Question. If x − 3 is a factor of x³ + 3x² + 3x + p, then the value of p is
(a) 0
(b) −63
(c) 10
(d) None of the options

Answer: B

Question. If a³ −3a²b + 3ab² − b³ is divided by (a − b), then the remainder is
(a) a² − ab + b²
(b) a² + ab + b²
(c) 1
(d) 0

Answer: D

Question. xⁿ − yⁿ is divisible by x + y, when n is_______.
(a) An odd positive integer
(b) An even positive integer
(c) An integer
(d) none of the options

Answer: B

Question. If the remainder when the polynomial f(x) is divided by x − 1, x + 1 are 6, 8 respectively then the remainder when f(x) is divided by (x − 1)(x + 1) is
(a) 7 − x
(b) 7 + x
(c) 8 − x
(d) 8 + x

Answer: A

Question. Let a, b be the zeros of the polynomial x² − px + r and ,α/2, 2β be the zeros of x²− qx + r. Then the value of r is −
(a) 2/9 (p−q)(2q−p) 
(b) 2/9 (q−p)(2p−q) 
(c) 2/9 (q −2p)(2q−p) 
(d) 2/9(2p−q)(2q−p)

Answer: D

Question. A real number is said to be algebraic if it satisfies a polynomial equation with integral coefficients. Which of the following numbers is not algebraic :
(a) 2/ 3
(b) 2
(c) 0
(d) π

Answer: D

Question. If two zeroes of p(x)= 2x⁴ + x³ – 14x² – 19x – 6 are –1 and –2, the other two zeroes are:
(a) 1/ 2 and – 3
(b) −1/ 2 and – 3
(c) −1/ 2 and 3
(d) none of the options

Answer: B

Question. If the zeroes of the polynomial x² + px + q are double in value to the zeroes of 2x² – 5x – 3, the values of p and q are respectively
(a) 5, 6
(b) 4, 7
(c) –5, –6
(d) –4, –7

Answer: B

Question. The sum and product of the zeroes of the quadratic equation given in example 1 are respectively
(a) 2, 4
(b) 5, –8
(c) 6, 8
(d) 2, –8

Answer: D

Question. If f(x) = ax² + bx + c is divided by (bx + c), then the remainder is_____.
(a) c²/b²
(b) ac²/b² + 2c
(c) f(−c/b)
(d) ac² +2b²c/b²

Answer: B

Question. If α,β are the zeros of the quadratic polynomial 4x² − 4x + 1, then α³ + β³ is −
(a) 1/ 4
(b) 1/ 8
(c) 16
(d) 32

Answer: A

Question. If c, d are zeros of x² − 10ax − 11b and a, b are zeros of x² − 10cx − 11d, then value of a + b + c + d is
(a) 1210
(b) − 1
(c) 2530
(d) − 11

Answer: A

Question. If the ratio of the roots of polynomial x² + bx + c is the same as that of the ratio of the roots of x² + qx + r, then
(a) br² = qc²
(b) cq² = rb²
(c) q²c² = b²r²
(d) bq = rc

Answer: B

Question. The value of k, if the sum of the zeroes of the polynomial x² – (k + 6) x + 2 (2k – 1) is half of their product is
(a) 7
(b) 11
(c) 12
(d) none of the options

Answer: A

Question. A quadratic equation x² – 2x – 8 is given. The zeroes of it are
(a) –2 and 4
(b) 3 and 5
(c) 1 and 6
(d) none of the options

Answer: A

Question. If 7 + 3x is a factor of 3x³ + 7x, then the remainder is
(a) 490/ 9
(b) −490/ 9
(c) 470/ 9
(d) None

Answer: B

Question. The remainder when f(x) = 3x⁴ + 2x³ −x2/3 −x/9 + 2/27 is divided by g(x) = x + 2/ 3 is
(a) −1
(b) 1
(c) 0
(d) −2

Answer: B

Question. The value of k for which (–4) is a zero of the polynomial x² – x – (2k + 2) is
(a) 2
(b) –6
(c) 9
(d) 8

Answer: B

Question. The sum and product of zeroes of the quadratic equation given in example 3 are respectively
(a) 2, 3/4
(b) 0, 1/8
(c) 1, 1/4
(d) none of the options

Answer: B

Question. When x200 + 1 is divided by x² + 1, the remainder is equal to −
(a) x + 2
(b) 2x − 1
(c) 2
(d) − 1

Answer: B

Question. If a (p + q)² + 2bpq + c = 0 and also a(q + r)² + 2bqr + c = 0 then pr is equal to −
(a) p² + a/ c
(b) q² +c/a
(c) p² +q/b
(d) q² +a/c

Answer: B

Question. If a + b = 4 and a³ + b³ = 44, then a,b are the zeros of the polynomial.
(a) 2x² − 7x + 6
(b) 3x² + 9x + 11
(c) 9x² − 27x + 20
(d) 3x² − 12x + 5

Answer: D

Question. The remainder when 1 + x + x² + x³ + ..........+ x2006 is divided by x− 1 is
(a) 2005
(b) 2006
(c) 2007
(d) 2008

Answer: C

Question. The quadratic polynomial whose zeros are twice the zeros of 2x² − 5x + 2 = 0 is −
(a) 8x² − 10x + 2
(b) x² − 5x + 4
(c) 2x² − 5x + 2
(d) x² − 10x + 6

Answer: B

Question. If one zero of the polynomial ax² + bx + c is posi- tive and the other negative then (a,b,c ∈R, a ≠ 0)
(a) a and b are of opposite signs.
(b) a and c are of opposite signs.
(c) b and c are of opposite signs.
(d) a,b,c are all of the same sign.

Answer: B

One word Question :

Question. Find the zeroes of the polynomial 9x² – 25.
Answer: ± 5/3

Question. For what value of x, both the polynomials p(x) – x² – x – 6 and q(x) – x² – 2x –15 becomes zero.
Answer: x = 3

Question. If α, β are the zeroes of quadratic polynomial x² – 3x + 2, form a quadratic polynomial whose zeroes are –α, and –β .
Answer: k (x² + 3x + 2)

Question. How many maximum zeroes will the polynomial 3x³ + 6x² – 7 can have ?
Answer: 3