$$x^9-3 = 0$$
Answer
$$ \begin{matrix}x_1 = 1.12983 & x_2 = 0.8655+0.72624i & x_3 = 0.8655-0.72624i \\[1 em] x_4 = -0.56492+0.97846i & x_5 = -0.56492-0.97846i & x_6 = -1.06169+0.38642i \\[1 em] x_7 = -1.06169-0.38642i & x_8 = 0.19619+1.11267i & x_9 = 0.19619-1.11267i \end{matrix} $$
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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