$$x^4-x-1 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.72449 & x_2 = 1.22074 & x_3 = -0.24813+1.03398i \\[1 em] x_4 = -0.24813-1.03398i & \\[1 em] \end{matrix} $$
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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