Find roots of polynomial $$ p(x) = \frac{2}{5}x^2+\frac{48}{5}x-400 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 21.8231\\[1 em]x_2 &= -45.8231 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 5 } $.
$$ \begin{aligned} \frac{2}{5}x^2+\frac{48}{5}x-400 & = 0 ~~~ / \cdot \color{blue}{ 5 } \\[1 em] 2x^2+48x-2000 & = 0 \end{aligned} $$Step 2:
The solutions of $ 2x^2+48x-2000 = 0 $ are: $ x = -12-2 \sqrt{ 286 } ~ \text{and} ~ x = -12+2 \sqrt{ 286 }$.
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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