Find roots of polynomial $$ p(x) = x^5+3x^4+2x^3+x^2+5x+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.4219\\[1 em]x_2 &= -1.8419+0.5598i\\[1 em]x_3 &= -1.8419-0.5598i\\[1 em]x_4 &= 0.5528+0.9867i\\[1 em]x_5 &= 0.5528-0.9867i \end{aligned} $$Explanation
Polynomial $ x^5+3x^4+2x^3+x^2+5x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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