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Question

If α,β are the roots of the equation x2+x15=0 then find α+βα1+β1

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Solution

The given equation is x2+x15=0

Here a=1,b=1,c=15

Sum of the roots=α+β=ba=11=1

Product of the roots=αβ=ca=151=15

α+βα1+β1

=α+β1α+1β

=α+βα+βαβ

=αβ(α+β)α+β

=αβ

=15

Hence, the required value is 15

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