$$x^4-8x^2+x+12 = 0$$
Answer
$$ \begin{matrix}x_1 = 1.56155 & x_2 = -1.30278 & x_3 = 2.30278 \\[1 em] x_4 = -2.56155 & \\[1 em] \end{matrix} $$
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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