The method differs depending on your PC and graphics card settings. For AMD for example, you can adjust different resolutions from the Catalyst Center. For Ubuntu, you can use console commands to access nVidia settings. Check out a forum thread for this question here:
http://ubuntuforums.org/showthread.php?t=772883
For Windows legacy versions, there's a thread which deals with that same question worth checking out here:
http://www.cnet.com/forums/discussions/1-monitor-2-desktops-with-different-resolutions-297146/
You can also use 3rd party software to configure resolution like:
http://www.makeuseof.com/tag/finally-get-two-functional-desktops-with-actual-multiple-monitors/
And here's a good list of programs that allow you to customize virtual desktops:
http://www.howtogeek.com/130650/the-best-free-programs-for-using-virtual-desktops-in-windows/