Well it would work when you run dual graphics, because dual graphics is just like crossfire where two cards work together
. However by looking at HP specs I don't think you can dual graphic your system, I don't have this HP but I just go by the specification they provide. It's better not to risk to waste your money
. That's what bad of buying prebuild. However you can get a 6770 which should support 4 monitors. Here is it:http://www.amazon.com/Sapphire-Radeon-DisplayPort-PCI-Express-100328FLEX/dp/B0056J9JAM
Oh yes, I forget, you need to upgrade your PSU, thanks striker 410!