Anyone that can guess the BIOS password, the boot loader password, or the root password can get full control of the machine. These should be different, unrelated, excellent passwords. Random text and digits are by far the best choice. You should never use a password that you think would return a hit from a search engine.
Guessing a user's password is only slightly less severe, as a hacker can obtain root access simply by waiting. The hacker waits for a "local exploit" for a flaw in the operating system to appear and uses that exploit before the machine is patched.
You should write down the BIOS password, the boot loader password and the root password. Now you don't need to remember them, so there is no reason for them not to be totally random, unrelated, excellent passwords. Fold the page, put it in an envelope and seal it.
Now we have turned a computer security problem into a physical security problem. We know how to solve those problems: locks, keys, alarms, safes, guards, regular inspections. If your site has staffed security then a good option is to leave the envelope in the care of the guard post with instructions to treat the envelope with the same procedures used for the site's master keys. Smaller sites can use a safe, a cash box or a locked drawer. A thief forcing a locked drawer still leaves shows more apparent signs of entry and more clues to their identity than is left by a hacker behind a modem.
These three passwords are an important corporate asset. If the machine is secure then forgetting the major passwords for the machine should result in a machine whose configuration cannot be altered by actions short of disassembly. You should have written procedures controlling the generation, storage, lifetime and use of major passwords.
But don't submit your proposed password to a search engine! Sending passwords in plain text across the Internet isn't good, nor the possibility of having them appear in the logs of a search engine.