Find roots of polynomial $$ p(x) = -4x^8+x^5+5x-4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.5143+0.8387i\\[1 em]x_2 &= 0.5143-0.8387i\\[1 em]x_3 &= -0.995+0.4765i\\[1 em]x_4 &= -0.995-0.4765i\\[1 em]x_5 &= -0.3436+1.053i\\[1 em]x_6 &= -0.3436-1.053i\\[1 em]x_7 &= 0.8243+0.112i\\[1 em]x_8 &= 0.8243-0.112i \end{aligned} $$Explanation
Polynomial $ -4x^8+x^5+5x-4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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