Find roots of polynomial $$ p(x) = \frac{1}{6}a^2+\frac{56}{3}+\frac{4}{2}-\frac{125}{12} $$

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

$$ \begin{aligned}a_1 &= \frac{\sqrt{ 246 }}{ 2 }i\\[1 em]a_2 &= - \frac{\sqrt{ 246 }}{ 2 }i \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 12 } $.

$$ \begin{aligned} \frac{1}{6}a^2+\frac{56}{3}+\frac{4}{2}-\frac{125}{12} & = 0 ~~~ / \cdot \color{blue}{ 12 } \\[1 em] 2a^2+224+24-125 & = 0 \end{aligned} $$

Step 2:

Combine like terms:

$$ 2a^2+ \color{blue}{224} + \color{red}{24} \color{red}{-125} = 2a^2+ \color{red}{123} $$

Step 3:

The solutions of $ 2a^2+123 = 0 $ are: $ a = \dfrac{\sqrt{ 246 }}{ 2 } i ~ \text{and} ~ a = - \dfrac{\sqrt{ 246 }}{ 2 } i $.

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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