Question
Find roots of polynomial $$ p(x) = m^3-3m^2-2m $$
Answer
The roots of polynomial $ p(m) $ are:
$$ \begin{aligned}m_1 &= 0\\[1 em]m_2 &= 3.5616\\[1 em]m_3 &= -0.5616 \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ m }$ from $ m^3-3m^2-2m $ and solve two separate equations:
$$ \begin{aligned} m^3-3m^2-2m & = 0\\[1 em] \color{blue}{ m }\cdot ( m^2-3m-2 ) & = 0 \\[1 em] \color{blue}{ m = 0} ~~ \text{or} ~~ m^2-3m-2 & = 0 \end{aligned} $$One solution is $ \color{blue}{ m = 0 } $. Use second equation to find the remaining roots.
Step 2:
The solutions of $ m^2-3m-2 = 0 $ are: $ m = \dfrac{ 3 }{ 2 }-\dfrac{\sqrt{ 17 }}{ 2 } ~ \text{and} ~ m = \dfrac{ 3 }{ 2 }+\dfrac{\sqrt{ 17 }}{ 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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