Find roots of polynomial $$ p(x) = m^2-\frac{6}{3}-16 $$
Answer
The roots of polynomial $ p(m) $ are:
$$ \begin{aligned}m_1 &= 3 \sqrt{ 2 }\\[1 em]m_2 &= -3 \sqrt{ 2 } \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 3 } $.
$$ \begin{aligned} m^2-\frac{6}{3}-16 & = 0 ~~~ / \cdot \color{blue}{ 3 } \\[1 em] 3m^2-6-48 & = 0 \end{aligned} $$Step 2:
Combine like terms:
$$ 3m^2 \color{blue}{-6} \color{blue}{-48} = 3m^2 \color{blue}{-54} $$Step 3:
The solutions of $ 3m^2-54 = 0 $ are: $ m = -3 \sqrt{ 2 } ~ \text{and} ~ m = 3 \sqrt{ 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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