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

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

$$ \begin{aligned}l_1 &= 0\\[1 em]l_2 &= 2\\[1 em]l_3 &= -1 \end{aligned} $$

Step 1:

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

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

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

Step 2:

The solutions of $ l^2-l-2 = 0 $ are: $ l = -1 ~ \text{and} ~ l = 2$.

You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.

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