Question 974021
The discriminant must be negative.
{{{(-2p)^2-4*q<0}}}
{{{4p^2-4q<0}}}
{{{p^2-q<0}}}
{{{p^2<q}}}
{{{q>p^2}}}


That may or may not be too helpful for your second question, and you might want to ask that again in another help posting request.  Before doing that, try solving {{{x^2-px+p^2-1>0}}} and see what you find.  (General solution for a quadratic equation).