Find roots of polynomial $$ p(x) = x^8+2x^3-x^2-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.8882\\[1 em]x_2 &= -1.2681\\[1 em]x_3 &= -0.2543+0.6814i\\[1 em]x_4 &= -0.2543-0.6814i\\[1 em]x_5 &= -0.4096+1.0427i\\[1 em]x_6 &= -0.4096-1.0427i\\[1 em]x_7 &= 0.8538+0.78i\\[1 em]x_8 &= 0.8538-0.78i \end{aligned} $$Explanation
Polynomial $ x^8+2x^3-x^2-1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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