$$x^4-x^2-x = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 1.32472 & x_3 = -0.66236+0.56228i \\[1 em] x_4 = -0.66236-0.56228i & \\[1 em] \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ x^{4}-x^{2}-x = 0 } $, first we need to factor our $ x $.
$$ x^{4}-x^{2}-x = x \left( x^{3}-x-1 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ x^{3}-x-1 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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