The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8007\\[1 em]x_2 &= 15.8171\\[1 em]x_3 &= 0.4918+1.2858i\\[1 em]x_4 &= 0.4918-1.2858i \end{aligned} $$Polynomial $ x^4-16x^3+4x^2-16x-24 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.