Find roots of polynomial $$ p(x) = -5x^4+1215000-41006250000 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 212.7903+212.7903i\\[1 em]x_2 &= 212.7903-212.7903i\\[1 em]x_3 &= -212.7903+212.7903i\\[1 em]x_4 &= -212.7903-212.7903i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ -5x^4+ \color{blue}{1215000} \color{blue}{-41006250000} = -5x^4 \color{blue}{-41005035000} $$Step 2:
Polynomial $ -5x^4-41005035000 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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