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If the sum of the reciprocals of the roots of the quadratic 3x^2 + 7x + k = 0 is \(1\), what is k?

 May 13, 2022
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Note that k CANNOT be equal to zero.

 

One root is \(x = {-7 + \sqrt{49-12k} \over 6}\), while the other is \(x = {-7 - \sqrt{49-12k} \over 6}\).

 

Their reciprocals are \(6 \over -7+\sqrt{49-12k}\) and \(6 \over -7-\sqrt{49-12k}\).

 

Adding those gives this nice expression: - \(7 \over k\) 

This is equal to one.

 

-7/k = 1

k = -7

 May 13, 2022

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