Find roots of polynomial $$ p(x) = x^5+x^4+3x^3+3x^2+6x+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7502\\[1 em]x_2 &= -0.7383+1.2851i\\[1 em]x_3 &= -0.7383-1.2851i\\[1 em]x_4 &= 0.6134+1.4323i\\[1 em]x_5 &= 0.6134-1.4323i \end{aligned} $$Explanation
Polynomial $ x^5+x^4+3x^3+3x^2+6x+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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