Find roots of polynomial $$ p(x) = s^5+s^4+10s^3+10s^2+20s+5 $$
Answer
The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= -0.2781\\[1 em]s_2 &= -0.5105+1.4297i\\[1 em]s_3 &= -0.5105-1.4297i\\[1 em]s_4 &= 0.1496+2.7888i\\[1 em]s_5 &= 0.1496-2.7888i \end{aligned} $$Explanation
Polynomial $ s^5+s^4+10s^3+10s^2+20s+5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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