Answer
$0$; $-4- 7\ i$; $-4+ 7\ i$
Work Step by Step
Given \begin{equation}
h^3+8 h^2+65 h=0.
\end{equation} This equation can be best solved by using the quadratic formula after factoring out $h$: \begin{equation}
\begin{aligned}
h^3+8 h^2+65 h&=0\\
h\left(h^2+8 h+65\right)&=0\\
h& = 0\\
h^2+8 h+65&= 0\\
h&=\frac{-8 \pm \sqrt{8^2-4 \cdot 1 \cdot 65}}{2 \cdot 1}\\
b&=\frac{-8 \pm 14 i}{2 }\\
&=-4\pm 7\ i.
\end{aligned}
\end{equation} The solution is \begin{equation}
h= 0\quad , h=-4\pm 7\ i.
\end{equation}
