When you set up a skeleton mysql system with mysql_install_db, the root account is created without a password.
So, to execute the command to change the password, you don't do this:
#mysqladmin -uroot -ppassword'new-password'
you do this
#mysqladmin -u root password flub2stickle
the root password should now be flub2stickle, and the password will be required for any further use of mysqladmin.
The next step is to forget the password you just entered.