Find roots of polynomial $$ p(x) = 2x^8+7x^7+20x^6+5x^5+3x^4+2x^3+3x^2-5x-7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7427\\[1 em]x_2 &= 0.7733\\[1 em]x_3 &= 0.4216+0.797i\\[1 em]x_4 &= 0.4216-0.797i\\[1 em]x_5 &= -0.5496+0.72i\\[1 em]x_6 &= -0.5496-0.72i\\[1 em]x_7 &= -1.6373+2.541i\\[1 em]x_8 &= -1.6373-2.541i \end{aligned} $$Explanation
Polynomial $ 2x^8+7x^7+20x^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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