Question
Find roots of polynomial $$ p(x) = -\frac{2}{3}x^2-8x-25 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -6+\dfrac{\sqrt{ 6 }}{ 2 }i\\[1 em]x_2 &= -6- \dfrac{\sqrt{ 6 }}{ 2 }i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 3 } $.
$$ \begin{aligned} -\frac{2}{3}x^2-8x-25 & = 0 ~~~ / \cdot \color{blue}{ 3 } \\[1 em] -2x^2-24x-75 & = 0 \end{aligned} $$Step 2:
The solutions of $ -2x^2-24x-75 = 0 $ are: $ x = -6+\dfrac{\sqrt{ 6 }}{ 2 }i ~ \text{and} ~ x = -6-\dfrac{\sqrt{ 6 }}{ 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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