$$x^3+x-1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.68233 & x_2 = -0.34116+1.16154i & x_3 = -0.34116-1.16154i \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Polynomial Equations Solver