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Question

If one root of polynomial f(x)=5x2+13x+k is reciprocal of the other then find the value of k.

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Solution

We have, p(x)=5x2+13x+k
Let first root be α, then other root =1α
Now, products of the roots =ConstanttermCoeff.ofx2
α×1α=k5
1=k5
k=5

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