Answer
$\frac{c}{a}$
Work Step by Step
The solutions of the quadratic equation $ax^{2}+bx+c = 0$ are
$\frac{-b+\sqrt (b^{2}-4ac)}{2a}$ and $\frac{-b-\sqrt (b^{2}-4ac)}{2a}$
Product of these solutions is
$=(\frac{-b+\sqrt (b^{2}-4ac)}{2a})$ $(\frac{-b-\sqrt (b^{2}-4ac)}{2a})$
$= \frac{(-b+\sqrt (b^{2}-4ac))(-b-\sqrt (b^{2}-4ac))}{4a^{2}}$
Using $(a+b)(a-b)=(a^{2}-b^{2})$ formula,
$= \frac{(-b)^{2}-(\sqrt (b^{2}-4ac))^{2}}{4a^{2}}$
$= \frac{b^{2}-(b^{2}-4ac)}{4a^{2}}$
$= \frac{b^{2}-b^{2}+4ac}{4a^{2}}$
$= \frac{4ac}{4a^{2}}$
$= \frac{c}{a}$
