I would appreciate if somebody could help me with the following problem.I am not good at quartic equations,so could not attempt much.
Q:The number of integral values of $p$ for which the equation $x^4+4x^3-8x^2+p=0$ has all 4 real roots.
Let $\alpha,\beta,\gamma,\delta $ are four real roots.
According to Vieta's formula
$\alpha+\beta+\gamma+\delta=-4$
$\alpha\beta+\alpha\gamma+\alpha\delta+\beta\gamma+\beta\delta+\gamma\delta=-8$
$\alpha\beta\gamma+\alpha\beta\delta+\alpha\gamma\delta+\beta\gamma\delta=0$
$\alpha\beta\gamma\delta=p$
then i got stuck..what to do?
Thanks in advance.