The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 3.8233i\\[1 em]x_2 &= -3.8233i\\[1 em]x_3 &= 6.8105i\\[1 em]x_4 &= -6.8105i \end{aligned} $$Polynomial $ x^4+61x^2+678 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.