Polynomials - Olympiad Level MCQ, Class 10 Mathematics

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

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 –

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 –

If α,β are zeros of ax² + bx + c then zeros of a3x² + abcx + c³ are –

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 –

When x²⁰⁰ + 1 is divided by x² + 1, the remainder is equal to –

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

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 :

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 –

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

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

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 –

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 –

If the roots of the polynomial ax² + bx + c are of the form  and   then the value of (a + b + c)² is–

If α, β and γ are the zeros of the polynomial x³ + a₀x² + a₁x + a₂, then (1 – α²) (1 – β²) (1 – γ²) is

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 –

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–

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

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) :

The condition that x³ – ax² + bx – c = 0 may have two of the roots equal to each other but of opposite signs is:

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 –

If one zero of the polynomial ax² + bx + c is positive and the other negative then (a,b,c εR, a = 0)

If α,β are the zeros of the polynomial x² – px + q, then   is equal to –

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

If α,β are zeros of ax² + bx + c, ac =  0, then zeros of cx² + bx + a are –

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 :

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

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

If the sum of zeros of the polynomial p(x) = kx³ – 5x² – 11x – 3 is 2, then k is equal to :

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

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

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