Answer
The roots of the polynomial equation are $x=-\frac{1}{2}\ ,x=\frac{2}{3}\ ,$ and $x=\frac{7}{2}$.
Work Step by Step
Consider the polynomial equation $\left( 2x+1 \right){{\left( 3x-2 \right)}^{3}}\left( 2x-7 \right)=0$
Simplify:
$\begin{align}
& \left( 2x+1 \right){{\left( 3x-2 \right)}^{3}}\left( 2x-7 \right)=0 \\
& x=\frac{-1}{2},\frac{2}{3},\frac{7}{2} \\
\end{align}$
Hence, the roots of the polynomial equation $\left( 2x+1 \right){{\left( 3x-2 \right)}^{3}}\left( 2x-7 \right)=0$ are $x=-\frac{1}{2}\ ,x=\frac{2}{3}\ ,$ and $x=\frac{7}{2}$ .
