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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

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

Grade:

1 Answers

askiitian.expert- chandra sekhar
10 Points
12 years ago

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


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