Find roots of polynomial $$ p(x) = -\frac{1}{15}x+2x^2+4 $$

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

$$ \begin{aligned}x_1 &= \frac{ 1 }{ 60 }+\frac{\sqrt{ 7199 }}{ 60 }i\\[1 em]x_2 &= \frac{ 1 }{ 60 }- \frac{\sqrt{ 7199 }}{ 60 }i \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 15 } $.

$$ \begin{aligned} -\frac{1}{15}x+2x^2+4 & = 0 ~~~ / \cdot \color{blue}{ 15 } \\[1 em] -x+30x^2+60 & = 0 \end{aligned} $$

Step 2:

Write polynomial in descending order

$$ \begin{aligned} -x+30x^2+60 & = 0\\[1 em] 30x^2-x+60 & = 0 \end{aligned} $$

Step 3:

The solutions of $ 30x^2-x+60 = 0 $ are: $ x = \dfrac{ 1 }{ 60 }+\dfrac{\sqrt{ 7199 }}{ 60 }i ~ \text{and} ~ x = \dfrac{ 1 }{ 60 }-\dfrac{\sqrt{ 7199 }}{ 60 }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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