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anurag singhal Grade:
        
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
8 years ago

Answers : (1)

askiitian.expert- chandra sekhar
10 Points
										

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



8 years ago
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