Find roots of polynomial $$ p(x) = x^6-13x^5+106x^4-529x^3+863x^2-744x-1378 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7734\\[1 em]x_2 &= 6.5867\\[1 em]x_3 &= 1.3372+1.8463i\\[1 em]x_4 &= 1.3372-1.8463i\\[1 em]x_5 &= 2.2561+6.8528i\\[1 em]x_6 &= 2.2561-6.8528i \end{aligned} $$Explanation
Polynomial $ x^6-13x^5+106x^4-529x^3+863x^2-744x-1378 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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