# 1965 AHSME Problems/Problem 7

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Using Vieta's formulas, we can write the sum of the roots of any quadratic equation in the form $ax^2+bx+c = 0$ 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 $\frac {-b}{c}$ => $\box{a}$ (Error compiling LaTeX. ! Missing number, treated as zero.).