Problem creating root password MySQL in FC6

[Barry Yu <barryyu-cts@xxxxxxxxxxxxx>]

In FC6, first time to start MySQL and try to create passwor for root 
user but failed, I login as root and did the following commands;

[root@localhost <mailto:root@localhost> ~]#

service mysqld start

           Starting MySQL:          [OK]

[root@localhost ~]# mysqladmin -u root password mypassword123

mysqladmin: connect to server at 'localhost' failed

error: 'Access denied for user 'root'@'localhost' (using password: NO)'

First time and completely new in MySQL, did I miss something? Need help.