Find roots of polynomial $$ p(x) = x^6+16x^5+103x^4+420x^3-808x^2+1644x+1196 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.5451\\[1 em]x_2 &= -10.8179\\[1 em]x_3 &= 1.1879+1.4537i\\[1 em]x_4 &= 1.1879-1.4537i\\[1 em]x_5 &= -3.5064+6.7271i\\[1 em]x_6 &= -3.5064-6.7271i \end{aligned} $$Explanation
Polynomial $ x^6+16x^5+103x^4+420x^3-808x^2+1644x+1196 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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