Find roots of polynomial $$ p(x) = -a^2-2a $$

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

$$ \begin{aligned}a_1 &= 0\\[1 em]a_2 &= -2 \end{aligned} $$

Step 1:

Factor out $ \color{blue}{ -a }$ from $ -a^2-2a $ and solve two separate equations:

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

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

Step 2:

To find the second zero, solve equation $ a+2 = 0 $

$$ \begin{aligned} a+2 & = 0 \\[1 em] a & = -2 \end{aligned} $$

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