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:
$$ \begin{aligned}x_1 &= 0.8503\\[1 em]x_2 &= -3.6017\\[1 em]x_3 &= -0.7791+0.3088i\\[1 em]x_4 &= -0.7791-0.3088i\\[1 em]x_5 &= -0.202+1.0982i\\[1 em]x_6 &= -0.202-1.0982i\\[1 em]x_7 &= 0.6067+0.968i\\[1 em]x_8 &= 0.6067-0.968i \end{aligned} $$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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