$$9x^8-52x^4+64 = 0$$
Answer
$$ \begin{matrix}x_1 = 1.41421 & x_2 = -1.1547 & x_3 = 1.1547 \\[1 em] x_4 = -1.41421 & x_5 = 1.1547i & x_6 = -1.1547i \\[1 em] x_7 = 1.41421i & x_8 = -1.41421i \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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