Polynomials - Olympiad Level MCQ, Class 10 Mathematics


35 Questions MCQ Test Olympiad Preparation for Class 10 | Polynomials - Olympiad Level MCQ, Class 10 Mathematics


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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. The solved questions answers in this Polynomials - Olympiad Level MCQ, Class 10 Mathematics quiz give you a good mix of easy questions and tough questions. Class 10 students definitely take this Polynomials - Olympiad Level MCQ, Class 10 Mathematics exercise for a better result in the exam. You can find other Polynomials - Olympiad Level MCQ, Class 10 Mathematics extra questions, long questions & short questions for Class 10 on EduRev as well by searching above.
QUESTION: 1

If α,β and γ are the zeros of the polynomial 2x3 – 6x2 – 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 ax2 + 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                x2 - 3x - 2

QUESTION: 3

  If x + 2 is a factor of x3 – 2ax2 + 16, then value of a is

Solution:
QUESTION: 4

If α,β and γ are the zeros of the polynomial f(x) = x3 + px2 – pqrx + r, then   =

Solution:
QUESTION: 5

If the parabola f(x) = ax2 + 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) = x2 + px + 1 and c, d are the zeros of f(x) = x2 + 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+ bx + c then zeros of a3x2 + abcx + c3 are –

Solution:
QUESTION: 8

Let α,β be the zeros of the polynomial x2 – px + r and    be the zeros of x2 – qx + r. Then the value
of r is –

Solution:
QUESTION: 9

When x200 + 1 is divided by x2 + 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 ax2 + bx + c, then value of (1 + α + α2) (1 + β + β2)  is :

Solution:
QUESTION: 12

Two complex numbers α and β are such that α + β = 2 and α4 + β4 = 272, then the polynomial whose zeros
are α and β is –

Solution:
QUESTION: 13

If 2 and 3 are the zeros of f(x) = 2x3 + mx2 – 13x + n, then the values of m and n are respectively –

Solution:
QUESTION: 14

If α,β are the zeros of the polynomial 6x2 + 6px + p2, then the polynomial whose zeros are (α + β)2 and (α - β)2 is

Solution:
QUESTION: 15

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 –

Solution:
QUESTION: 16

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 –

Solution:
QUESTION: 17

If the roots of the polynomial ax2 + 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 x3 + a0x2 + a1x + a2, then (1 – α2) (1 – β2) (1 – γ2) is

Solution:
QUESTION: 19

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 –

Solution:
QUESTION: 20

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–

Solution:
QUESTION: 21

If α,β are the roots of ax2 + bx + c and α + k, β + k are the roots of px2 + qx + r, then k =

Solution:
QUESTION: 22

If α,β are the roots of the polynomial x2 – px + q, then the quadratic polynomial, the roots of which are (α2– β2) (α3 – β3) and (α3β2 + α2β3) :

Solution:
QUESTION: 23

The condition that x3 – ax2 + 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 x2 + bx + ac are α,β and roots of the polynomial x2 + ax + bc are α,γ then the values of α,β,γ respectively are –

Solution:
QUESTION: 25

If one zero of the polynomial ax2 + 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 x2 – px + q, then   is equal to –

Solution:
QUESTION: 27

If α,β are the zeros of the polynomial x2 – px + 36 and α2 + β2 = 9, then p =

Solution:
QUESTION: 28

If α,β are zeros of ax2 + bx + c, ac =  0, then zeros of cx2 + 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) = kx3 – 5x2 – 11x – 3 is 2, then k is equal to :

Solution:
QUESTION: 33

If f(x) = 4x3 – 6x2 + 5x – 1 and α, β and γ are its zeros, then αβγ  =

Solution:
QUESTION: 34

Consider f(x) = 8x4 – 2x2 + 6x – 5 and α,β,γ,δ are it's zeros then α + β + γ + δ =

Solution:
QUESTION: 35

If x2 – ax + b = 0 and x2 – px + q = 0 have a root in common and the second equation has equal roots, then –

Solution: