Find roots of polynomial $$ p(x) = s^6+7s^5+2s^4+9s^3+10s^2+12s+5 $$
Answer
The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= -0.5297\\[1 em]s_2 &= -6.8738\\[1 em]s_3 &= -0.4496+0.7729i\\[1 em]s_4 &= -0.4496-0.7729i\\[1 em]s_5 &= 0.6513+1.1374i\\[1 em]s_6 &= 0.6513-1.1374i \end{aligned} $$Explanation
Polynomial $ s^6+7s^5+2s^4+9s^3+10s^2+12s+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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