Answer
$\sum x=-3$
Work Step by Step
Given that $x_1=-2$, we divide the polynomial $f(x)=x^3+5x^2+5x-2$ by $x+2$:
$\begin{array}{lllll}
\underline{-2}| & 1&5 & 5 &-2 \\
& & -2 & -6& 2\\
& -- & -- & -- & --\\
& 1 & 3 & -1& |\underline{0}
\end{array}$
We got:
$f(x)=(x+2)(x^{2} +3x-1)$
The solutions $x_2$ and $x_3$ are the zeros of the trinomial $x^2+3x-1$. We have:
$x_2+x_3=-\frac{3}{1}=-3$.
