The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.0899\\[1 em]x_2 &= 2.3202\\[1 em]x_3 &= 0.3848+1.1974i\\[1 em]x_4 &= 0.3848-1.1974i \end{aligned} $$Polynomial $ x^4-2x^3-4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.