Find roots of polynomial $$ p(x) = 2x^8-7x^7+x^6+5x^5+3x^4+2x^3+3x^2-5x-7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8211\\[1 em]x_2 &= 1.2064\\[1 em]x_3 &= 1.3446\\[1 em]x_4 &= 2.9803\\[1 em]x_5 &= 0.1248+0.9918i\\[1 em]x_6 &= 0.1248-0.9918i\\[1 em]x_7 &= -0.7299+0.5913i\\[1 em]x_8 &= -0.7299-0.5913i \end{aligned} $$Explanation
Polynomial $ 2x^8-7x^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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