Boot into single user mode (I'm not that familiar with Yellow Dog, but I think if you hit the tab key at the boot splash screen you should be able to select a single user mode or repair mode). Once you reach a prompt, reset the root password.
Immediately afterwards, check the last login times with last -i to see if there are any abnormal root logins and also check root's .bash_history to look for abnormal activity. Also check /etc/passwd for any strange users, users other than root with a UID of 0, or system users with valid login shells. The root password shouldn't just randomly change, the passwd file can become corrupted, but having just root's password change is highly suspicious and absolutely requires that you make sure the system hasn't been compromised somehow.
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