You would have the home account authorized on your work computer. You can authorize up to 5 computers per account.
The work computer would also retain it's authorization for the work itunes store account.
To authorize, launch itunes. Select Store from the pulldown menu on itunes.
Select Authorize this computer. It will prompt you for account and password.
I think things may be getting confused with terminology a bit. You can only sync an iPad with a single iTunes library on a single computer. That iTunes library, though, can have content from up to five iTunes Store accounts. So if you're purchasing content from a home account in the iTunes Store as well as from a work iTunes Store account, or you're using a single account but purchasing from both the home and work computers, then you can have it all on your iPad. You just need to get the content into iTunes on onto a single computer, whichever one you have decided to use to sync your iPad. If you need help moving content from one computer to the other, post back and we can help further with that.
Hope this helps.