Find roots of polynomial $$ p(x) = 8x^5-5x^4-2x^3-8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.2438\\[1 em]x_2 &= 0.4308+0.8665i\\[1 em]x_3 &= 0.4308-0.8665i\\[1 em]x_4 &= -0.7402+0.5575i\\[1 em]x_5 &= -0.7402-0.5575i \end{aligned} $$Explanation
Polynomial $ 8x^5-5x^4-2x^3-8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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