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Question

If one root of 5x2+13x+k=0 is the reciprocal of the other root, then find the value of k.


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Solution

Find the value of k.

Let α be one of the roots of the quadratic equation. So, as per the given condition, the other roots is 1α.

Product of the roots of quadratic equation is

α×1α=k5k=5

Hence, the value of k is 5.


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