The password is stored in only one place, /etc/shadow, for every user account (look at /etc/passwd and /etc/shardow with an editor such as vi -- but don't mess with 'em).
So, log in as root and execute passwd; you'll be prompted for the new password and all is well that ends. If for some reason you have two accounts named "root" and "root-something-or-other" (for the zone), change 'em both using the passwe utility. It is highly unlikely that you actually will have a separate password for the zone but... who knows what evil lurks in the dark of night, eh.
Hope this helps some.