Find roots of polynomial $$ p(x) = 27x^8-56x^7-24x^5+25x^4-3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.5051\\[1 em]x_2 &= 2.1726\\[1 em]x_3 &= -0.0151+0.574i\\[1 em]x_4 &= -0.0151-0.574i\\[1 em]x_5 &= -0.4101+0.7195i\\[1 em]x_6 &= -0.4101-0.7195i\\[1 em]x_7 &= 0.6284+0.2299i\\[1 em]x_8 &= 0.6284-0.2299i \end{aligned} $$Explanation
Polynomial $ 27x^8-56x^7-24x^5+25x^4-3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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