Question
Find roots of polynomial $$ p(x) = 2m^4-5m^3-3m^2 $$
Answer
The roots of polynomial $ p(m) $ are:
$$ \begin{aligned}m_1 &= 0\\[1 em]m_2 &= 3\\[1 em]m_3 &= -\dfrac{ 1 }{ 2 } \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ m^2 }$ from $ 2m^4-5m^3-3m^2 $ and solve two separate equations:
$$ \begin{aligned} 2m^4-5m^3-3m^2 & = 0\\[1 em] \color{blue}{ m^2 }\cdot ( 2m^2-5m-3 ) & = 0 \\[1 em] \color{blue}{ m^2 = 0} ~~ \text{or} ~~ 2m^2-5m-3 & = 0 \end{aligned} $$One solution is $ \color{blue}{ m = 0 } $. Use second equation to find the remaining roots.
Step 2:
The solutions of $ 2m^2-5m-3 = 0 $ are: $ m = -\dfrac{ 1 }{ 2 } ~ \text{and} ~ m = 3$.
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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