Everybody seemed very confused by the story and extra information I gave so I will simply ask a very straightforward question. Irrespective of your personal opinion on the utility of doing so; how does a person change the root password?
Also, the apple help page that I linked originally, and that some of you additionally linked to does not actually say how to change the root password, it only says that it can be done.
Best Answer
If you can already log in on an account with administrator privileges (normal OS X account) and know its login password, you can reset the passwords of other admin accounts in System Preferences > Accounts. If you can't, you can reset the passwords of admin accounts in single user mode. See this question.
If you actually mean the password of the root user, it can be changed from /System/Library/CoreServices/Directory Utility.app/, but you have to be logged in on an admin account and know its login password.