Find roots of polynomial $$ p(x) = s^4+s^2+1 $$
Answer
The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= 0.5+0.866i\\[1 em]s_2 &= 0.5-0.866i\\[1 em]s_3 &= -0.5+0.866i\\[1 em]s_4 &= -0.5-0.866i \end{aligned} $$Explanation
Polynomial $ s^4+s^2+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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