The GeForce GTX 980 has support for a pretty interesting feature. While I'll go more about it in my review that I'll be posting soon, there's a way to let you run games at up to 4K resolution on displays with lower resolution.
Called Dynamic Super Resolution, a game can be set to 4K and the software will down sample the image to a resolution that your monitor supports. You do get a hit on performance, but picture quality can be improved from this technique.
Up until today, only the new Maxwell desktop cards supported it, but with the release of the 344.48 drivers, Kepler and Fermi desktop GPUs will be able to try this out as well.
I do suggest testing it on older games so you don't get a slide show when playing, and results will vary on how well it improves the graphics depending on the game.
Give it a try if you have one of the compatible cards.