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Question

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

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Solution

Let one root be α and the other root be 1α.

The given equation is 5x2 +13x + k = 0.

Product of roots = k5
α×1α=k51=k5k=5

Hence, the value of k is 5.

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