The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.8325\\[1 em]x_2 &= -0.8325\\[1 em]x_3 &= 1.2013i\\[1 em]x_4 &= -1.2013i \end{aligned} $$Polynomial $ 4x^4+3x^2-4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.