Answer
Proved
Work Step by Step
For the equation $a{{x}^{2}}+bx+c=0$, use the quadratic formula to solve.
$x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$
When there is one solution, the discriminant is 0.
So, ${{b}^{2}}-4ac$ is 0.
Therefore,
$\begin{align}
& x=\frac{-b\pm 0}{2a} \\
& =\frac{-b}{2a}
\end{align}$
Thus, the only solution of the equation $a{{x}^{2}}+bx+c=0$ is $-\frac{b}{2a}$.
