$$121c^4-44c^2+4 = 0$$
Answer
$$ \begin{matrix}c_1 = 0.4264 & c_2 = -0.4264 \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Polynomial Equations Solver