$$r^6+1 = 0$$
Answer
$$ \begin{matrix}r_1 = 0.86603+0.5i & r_2 = 0.86603-0.5i & r_3 = -0.86603+0.5i \\[1 em] r_4 = -0.86603-0.5i & r_5 = 1i & r_6 = -i \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
This page was created using
Polynomial Equations Solver