Find roots of polynomial $$ p(x) = x^8+4x^7+10x^6+2x^5+110x^4-106x+50 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.6095+0.071i\\[1 em]x_2 &= 0.6095-0.071i\\[1 em]x_3 &= -0.6427+0.8712i\\[1 em]x_4 &= -0.6427-0.8712i\\[1 em]x_5 &= 1.1287+2.3125i\\[1 em]x_6 &= 1.1287-2.3125i\\[1 em]x_7 &= -3.0955+2.7438i\\[1 em]x_8 &= -3.0955-2.7438i \end{aligned} $$Explanation
Polynomial $ x^8+4x^7+10x^6+2x^5+110x^4-106x+50 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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