Take complex roots and apply it to a new polynomial Polynomial $f(x)=x^3-x^2+x+18$ has three distinct complex roots $r_1$,$r_2$, and $r_3$. Denote by $g(x)$ the cubic polynomial with leading coeffecient $1$ such that $g(r_i+\frac{1}{r_i})=0$, for $i=1,2,3$. The value of $g(2)$ can be expressed in the form $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$. Compute the sum of $m$ and $n$.
$\textbf{Thoughts}$
I'm not sure how to approach this question in any way whatsoever. Help is much appreciated.

You might start with $$g(x) = (x - (r_1 + 1/r_1))(x - (r_2 + 1/r_2))(x - (r_3 + 1/r_3))$$
EDIT:
So $$ \eqalign{g(2) &= \frac{(r_1 - 1)^2 (r_2 - 1)^2 (r_3 - 1)^2}{r_1 r_2 r_3} \cr
&= \frac{f(1)^2}{r_1 r_2 r_3}}$$
