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