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Question

If α,β are the roots of the equation ax2+bx+c=0 then show that 1aα+b+1aβ+b=bac

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Solution

If α,β are the roots of the equation ax2+bx+c=0

then aα2+bα+c=0 and aβ2+bβ+c=0

α(aα+b)+c=0 and β(aβ+b)+c=0

(aα+b)=cα and (aβ+b)=cβ

L.H.S=1aα+b+1aβ+b

=αc+βc

=αβc

=(α+β)c

=(ba)c

=bac

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