Q1. The roots alpha and betaof quadratioc equation pxsquare+qx+r are real and of opposite sign .

the roots of alpha(x-beta)square+beta(x-alpha)square=0are

a) positive

b) neagative

c) real and of opposite sign

d) imaginary

α(x-β)²+β(x-α)²=0    ---(1)

Given α and β are real and of opposite sign

Therefore αβ= -ve

From equation 1

α(x²+β²-2xβ) + β(x²+α²-2αx)=0

(α+β)x²-4αβx+αβ(α+β)=0

product of the roots = αβ(α+β)/(α+β)= αβ = -ve

discriminant Δ=16 α²β²-4 αβ( α+β)² 

as 16 α²β² and ( α+β)² are positive and αβ is negative, Δ  is positive

so the roots of the equation are real and opposite in sign.

Ans: c