Find roots of polynomial $$ p(x) = 2x^8-5x^7+x^6+5x^5+3x^4+2x^3+3x^2-5x-7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8471\\[1 em]x_2 &= 1.0309\\[1 em]x_3 &= 0.1189+1.0267i\\[1 em]x_4 &= 0.1189-1.0267i\\[1 em]x_5 &= -0.7674+0.5929i\\[1 em]x_6 &= -0.7674-0.5929i\\[1 em]x_7 &= 1.8066+0.8522i\\[1 em]x_8 &= 1.8066-0.8522i \end{aligned} $$Explanation
Polynomial $ 2x^8-5x^7+x^6+5x^5+3x^4+2x^3+3x^2-5x-7 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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