Find roots of polynomial $$ p(x) = 2x^8+7x^7+x^6+11x^5+3x^4+2x^3+3x^2-5x-7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.8215\\[1 em]x_2 &= -3.7342\\[1 em]x_3 &= -0.7255+0.3208i\\[1 em]x_4 &= -0.7255-0.3208i\\[1 em]x_5 &= -0.0996+1.1565i\\[1 em]x_6 &= -0.0996-1.1565i\\[1 em]x_7 &= 0.5315+1.031i\\[1 em]x_8 &= 0.5315-1.031i \end{aligned} $$Explanation
Polynomial $ 2x^8+7x^7+x^6+11x^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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