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:
$$ \begin{aligned}x_1 &= 0.8809\\[1 em]x_2 &= -2.5979\\[1 em]x_3 &= -0.85+0.3068i\\[1 em]x_4 &= -0.85-0.3068i\\[1 em]x_5 &= -0.2076+1.1266i\\[1 em]x_6 &= -0.2076-1.1266i\\[1 em]x_7 &= 0.6661+0.9917i\\[1 em]x_8 &= 0.6661-0.9917i \end{aligned} $$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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