smc

Using Vieta's formulas, we can write the sum of the roots of any quadratic equation in the form $a{x}^2+bx+c=0$ as $\frac{-b}{a}$, and the product as $\frac{c}{a}$. If $r$ and $s$ are the roots, then the sum of the reciprocals of the roots is $\frac{1}{r}+\frac{1}{s}=\frac{r+s}{rs}$. Applying the formulas, we get $\frac{\frac{-b}{a}}{\frac{c}{a}}$, or $\frac{-b}{c}$ => $\boxed{-\frac{b}{c}}$.