Find roots of polynomial $$ p(x) = 2x^8+7x^7+x^6-8x^5+3x^4+2x^3+3x^2-5x-7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7561\\[1 em]x_2 &= 1.0355\\[1 em]x_3 &= -1.8824\\[1 em]x_4 &= -2.689\\[1 em]x_5 &= 0.7354+0.7296i\\[1 em]x_6 &= 0.7354-0.7296i\\[1 em]x_7 &= -0.3394+0.8413i\\[1 em]x_8 &= -0.3394-0.8413i \end{aligned} $$Explanation
Polynomial $ 2x^8+7x^7+x^6-8x^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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