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Question

Let x1, x2 be the roots of ax2+bx+c=0 and x1.x2<0, x1+x2 is non - zero. Roots of x1(xx2)2+x2(xx1)2=0 are


A

Negative

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B

Real and of opposite signs

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C

positive

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D

non real

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Solution

The correct option is B

Real and of opposite signs


Given x1(xx2)2+x2(xx1)2=0
x2(x1+x2)4x x1 x2+x1 x2(x1+x2)=0Δ=16 x21x224x1x2(x1+x2)2>0 ( x1x2<0 given)
Real roots
Also product of roots x1x2<0
Roots are of opposite sign


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