Answer
The roots of the polynomial function are $\left\{ -3,\frac{5}{2} \right\}$.
Work Step by Step
Let us consider the function $f\left( x \right)=2{{x}^{2}}+x-15$.
Equating the function to zero gives:
$\begin{align}
& 2{{x}^{2}}+x-15=0 \\
& {{x}^{2}}+3x-\frac{5}{2}x-\frac{15}{2}=0 \\
& \left( x+3 \right)\left( x-\frac{5}{2} \right)=0 \\
& x=-3,\frac{5}{2}
\end{align}$
Thus, the roots of the polynomial are $\left\{ -3,\,\,\frac{5}{2} \right\}$
