The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.7935+0.7935i\\[1 em]x_2 &= 0.7935-0.7935i\\[1 em]x_3 &= -0.7935+0.7935i\\[1 em]x_4 &= -0.7935-0.7935i\\[1 em]x_5 &= -1.0249+1.0249i\\[1 em]x_6 &= -1.0249-1.0249i\\[1 em]x_7 &= 1.0249+1.0249i\\[1 em]x_8 &= 1.0249-1.0249i \end{aligned} $$Polynomial $ x^8+6x^4+7 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.