$$s^4+176s^2+1024 = 0$$
Answer
$$ \begin{matrix}s_1 = 2.45446i & s_2 = -2.45446i & s_3 = 13.03747i \\[1 em] s_4 = -13.03747i & \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Polynomial Equations Solver