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This mock test of Polynomials - Olympiad Level MCQ, Class 10 Mathematics for Class 10 helps you for every Class 10 entrance exam.
This contains 35 Multiple Choice Questions for Class 10 Polynomials - Olympiad Level MCQ, Class 10 Mathematics (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If α,β and γ are the zeros of the polynomial 2x^{3} – 6x^{2} – 4x + 30, then the value of (αβ + βγ + γα) is

Solution:

QUESTION: 2

The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is –2 is :

Solution:

Sum of zeroes = 3

Product of zeroes = -2

Let the quadratic polynomial be ax^{2} + bx + c

Sum of zeroes = 3

-b/a = 3/1

So a = 1, b = -3

Product of zeroes = -2

c/a = -2/1

So a = 1, c = -2

Hence the quadratic polynomial will be x^{2} - 3x - 2

QUESTION: 3

If x + 2 is a factor of x^{3} – 2ax^{2} + 16, then value of a is

Solution:

QUESTION: 4

If α,β and γ are the zeros of the polynomial f(x) = x^{3} + px^{2} – pqrx + r, then =

Solution:

QUESTION: 5

If the parabola f(x) = ax^{2} + bx + c passes through the points (–1, 12), (0, 5) and (2, –3), the value of a + b + c is –

Solution:

QUESTION: 6

If a, b are the zeros of f(x) = x^{2} + px + 1 and c, d are the zeros of f(x) = x^{2} + qx + 1 the value of E = (a – c) (b – c) (a + d) (b + d) is –

Solution:

QUESTION: 7

If α,β are zeros of ax^{2 }+ bx + c then zeros of a3x^{2} + abcx + c^{3} are –

Solution:

QUESTION: 8

Let α,β be the zeros of the polynomial x^{2} – px + r and be the zeros of x^{2} – qx + r. Then the value

of r is –

Solution:

QUESTION: 9

When x^{200} + 1 is divided by x^{2} + 1, the remainder is equal to –

Solution:

QUESTION: 10

If a (p + q)^{2} + 2bpq + c = 0 and also a(q + r)^{2} + 2bqr + c = 0 then pr is equal to –

Solution:

QUESTION: 11

If a,b and c are not all equal and α and β be the zeros of the polynomial ax^{2} + bx + c, then value of (1 + α + α^{2}) (1 + β + β^{2}) is :

Solution:

QUESTION: 12

Two complex numbers α and β are such that α + β = 2 and α^{4} + β^{4} = 272, then the polynomial whose zeros

are α and β is –

Solution:

QUESTION: 13

If 2 and 3 are the zeros of f(x) = 2x^{3} + mx^{2} – 13x + n, then the values of m and n are respectively –

Solution:

QUESTION: 14

If α,β are the zeros of the polynomial 6x^{2} + 6px + p^{2}, then the polynomial whose zeros are (α + β)^{2} and (α - β)^{2} is

Solution:

QUESTION: 15

If c, d are zeros of x^{2} – 10ax – 11b and a, b are zeros of x^{2} – 10cx – 11d, then value of a + b + c + d is –

Solution:

QUESTION: 16

If the ratio of the roots of polynomial x^{2} + bx + c is the same as that of the ratio of the roots of x^{2} + qx + r, then –

Solution:

QUESTION: 17

If the roots of the polynomial ax^{2} + bx + c are of the form and then the value of (a + b + c)^{2} is–

Solution:

QUESTION: 18

If α, β and γ are the zeros of the polynomial x^{3} + a_{0}x^{2} + a_{1}x + a_{2}, then (1 – α^{2}) (1 – β^{2}) (1 – γ^{2}) is

Solution:

QUESTION: 19

If α,β,γ are the zeros of the polynomial x^{3} – 3x + 11, then the polynomial whose zeros are (α + β), (β + γ) and

(γ + α) is –

Solution:

QUESTION: 20

If α,β,γ are such that α + β + γ = 2, α^{2} + β^{2} + γ^{2} = 6, α^{3} + β^{3} + γ^{3} = 8, then α^{4} + β^{4} + γ^{4} is equal to–

Solution:

QUESTION: 21

If α,β are the roots of ax^{2} + bx + c and α + k, β + k are the roots of px^{2} + qx + r, then k =

Solution:

QUESTION: 22

If α,β are the roots of the polynomial x^{2} – px + q, then the quadratic polynomial, the roots of which are (α^{2}– β^{2}) (α^{3} – β^{3}) and (α^{3}β^{2} + α^{2}β^{3}) :

Solution:

QUESTION: 23

The condition that x^{3} – ax^{2} + bx – c = 0 may have two of the roots equal to each other but of opposite signs is:

Solution:

QUESTION: 24

If the roots of polynomial x^{2} + bx + ac are α,β and roots of the polynomial x^{2} + ax + bc are α,γ then the values of α,β,γ respectively are –

Solution:

QUESTION: 25

If one zero of the polynomial ax^{2} + bx + c is positive and the other negative then (a,b,c εR, a = 0)

Solution:

QUESTION: 26

If α,β are the zeros of the polynomial x^{2} – px + q, then is equal to –

Solution:

QUESTION: 27

If α,β are the zeros of the polynomial x^{2} – px + 36 and α^{2} + β^{2} = 9, then p =

Solution:

QUESTION: 28

If α,β are zeros of ax^{2} + bx + c, ac = 0, then zeros of cx^{2} + bx + a are –

Solution:

QUESTION: 29

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 :

Solution:

QUESTION: 30

The bi-quadraic polynomial whose zeros are 1, 2, 4/3, - 1 is :

Solution:

QUESTION: 31

The cubic polynomials whose zeros are 4,3/2 and – 2 is :

Solution:

QUESTION: 32

If the sum of zeros of the polynomial p(x) = kx^{3} – 5x^{2} – 11x – 3 is 2, then k is equal to :

Solution:

QUESTION: 33

If f(x) = 4x^{3} – 6x^{2} + 5x – 1 and α, β and γ are its zeros, then αβγ =

Solution:

QUESTION: 34

Consider f(x) = 8x^{4} – 2x^{2} + 6x – 5 and α,β,γ,δ are it's zeros then α + β + γ + δ =

Solution:

QUESTION: 35

If x^{2} – ax + b = 0 and x^{2} – px + q = 0 have a root in common and the second equation has equal roots, then –

Solution:

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