Reciprocal roots

Question

I have this question:

It is known that two of the roots of the equation $3x^3+x^2-kx+6=0$ are reciprocals of each other. What is the value of $k$?

How do I find $k$?

Answer 1

We know that $-6/3=x_1x_2x_3=1\cdot x_3$, hence $x=-2$ is a root. Now plug in.

PS: The other roots are $\frac16(5\pm i\sqrt{11})$.