Find roots of polynomial $$ p(x) = x^2+\frac{20}{3} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \frac{ 2 \sqrt{ 15}}{ 3 }i\\[1 em]x_2 &= -2 \frac{\sqrt{ 15 }}{ 3 }i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 3 } $.
$$ \begin{aligned} x^2+\frac{20}{3} & = 0 ~~~ / \cdot \color{blue}{ 3 } \\[1 em] 3x^2+20 & = 0 \end{aligned} $$Step 2:
The solutions of $ 3x^2+20 = 0 $ are: $ x = \dfrac{ 2 \sqrt{ 15}}{ 3 } i ~ \text{and} ~ x = -2 \dfrac{\sqrt{ 15 }}{ 3 } 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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