Find roots of polynomial $$ p(x) = s^5+3s^4+5s^3+4s^2+s+3 $$
Answer
The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= -1.6313\\[1 em]s_2 &= 0.2563+0.7201i\\[1 em]s_3 &= 0.2563-0.7201i\\[1 em]s_4 &= -0.9407+1.5042i\\[1 em]s_5 &= -0.9407-1.5042i \end{aligned} $$Explanation
Polynomial $ s^5+3s^4+5s^3+4s^2+s+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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