Find roots of polynomial $$ p(x) = 2x^8+7x^7+x^6-7x^5+3x^4+2x^3+3x^2-5x-7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7702\\[1 em]x_2 &= 1.0172\\[1 em]x_3 &= -1.7127\\[1 em]x_4 &= -2.8211\\[1 em]x_5 &= 0.7327+0.7454i\\[1 em]x_6 &= 0.7327-0.7454i\\[1 em]x_7 &= -0.3393+0.8551i\\[1 em]x_8 &= -0.3393-0.8551i \end{aligned} $$Explanation
Polynomial $ 2x^8+7x^7+x^6-7x^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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