If and are the real roots of and are the roots of

MATHEMATICS · Single correct · CBSE · Mathematics · Polynomials · Polynomials

Problem

\alpha

and

\beta

are the real roots of

x^2+px+q=0

and

\alpha^4,\beta^4

are the roots of

x^2-rx+s=0

. Then the equation

x^2-4qx+2q^2-r=0

has always (

\alpha\neq\beta,\ p\neq0,\ p,q,r,s\in\mathbb{R}

): (a) one positive and one negative root (b) two positive roots (c) two negative roots (d) can't say anything