Resolve a conditional expression including existsExists and forallForAll

edited title

Link

edited Mar 10, 2014 at 3:12

Resolve ana conditional expression including exists and forall

Source Link

asked Mar 10, 2014 at 3:05

I don't know the Resolve function exactly, especially when involved with Exists and ForAll, could you please help me in the following example?

$\forall C$, can we find some $x>0$, such that $$ c(x)=(C+2x)x^2+C^2x+2Cx^2+C\geq0, $$ and $$ C<-2x $$ holds at the sametime?