Find roots of polynomial $$ p(x) = x^5+5x^4+2x^3+4x^2+6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -4.7681\\[1 em]x_2 &= 0.535+0.7965i\\[1 em]x_3 &= 0.535-0.7965i\\[1 em]x_4 &= -0.651+0.9711i\\[1 em]x_5 &= -0.651-0.9711i \end{aligned} $$Explanation
Polynomial $ x^5+5x^4+2x^3+4x^2+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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