Answer
The roots of the polynomial equation are $x\ =\ 10$ , $x\ =\ -10$ , and $x\ =\ -\frac{5}{2}$.
Work Step by Step
$\begin{align}
& 2{{x}^{3}}\ +\ 5{{x}^{2}}\ -\ 200x\ -\ 500\ =\ 0 \\
& {{x}^{2}}\left( 2x+5 \right)-100\left( 2x+5 \right)=0 \\
& \left( {{x}^{2}}-100 \right)\left( 2x+5 \right)=0 \\
& x=\pm 10,\frac{-5}{2}
\end{align}$
Thus, the roots of the equation $2{{x}^{3}}\ +\ 5{{x}^{2}}\ -\ 200x\ -\ 500\ =\ 0$ are $x=\pm 10,\frac{-5}{2}$.
