+0

# Algebra

0
38
1

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

#1
+225
+1

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