Find roots of polynomial $$ p(x) = x^2+500x^2-4000 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \frac{ 20 \sqrt{ 5010}}{ 501 }\\[1 em]x_2 &= -20 \frac{\sqrt{ 5010 }}{ 501 } \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{x^2} + \color{blue}{500x^2} -4000 = \color{blue}{501x^2} -4000 $$Step 2:
The solutions of $ 501x^2-4000 = 0 $ are: $ x = -20 \dfrac{\sqrt{ 5010 }}{ 501 } ~ \text{and} ~ x = \dfrac{ 20 \sqrt{ 5010}}{ 501 }$.
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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