$$x^3-x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = -1.32472 & x_2 = 0.66236+0.56228i & x_3 = 0.66236-0.56228i \end{matrix} $$
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