Find roots of polynomial $$ p(x) = s^3+s^2 $$

The roots of polynomial $ p(s) $ are:

$$ \begin{aligned}s_1 &= 0\\[1 em]s_2 &= -1 \end{aligned} $$

Step 1:

Factor out $ \color{blue}{ s^2 }$ from $ s^3+s^2 $ and solve two separate equations:

$$ \begin{aligned} s^3+s^2 & = 0\\[1 em] \color{blue}{ s^2 }\cdot ( s+1 ) & = 0 \\[1 em] \color{blue}{ s^2 = 0} ~~ \text{or} ~~ s+1 & = 0 \end{aligned} $$

One solution is $ \color{blue}{ s = 0 } $. Use second equation to find the remaining roots.

Step 2:

To find the last zero, solve equation $ s+1 = 0 $

$$ \begin{aligned} s+1 & = 0 \\[1 em] s & = -1 \end{aligned} $$

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