The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.5616\\[1 em]x_2 &= -1.3028\\[1 em]x_3 &= 2.3028\\[1 em]x_4 &= -2.5616 \end{aligned} $$Polynomial $ x^4-8x^2+x+12 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.