To change the MySQL root user password do the following:
1. Open a CommandLine (Linux or Windows or Mac, doesnt matter)
2. Navigate to the directory, where mysqladmin is located
3. Enter the following into the commandline:
mysqladmin -u root password YourPassword
where YourPassword is the new password of your choice for the MySQL root user.
On Linux, if mysqladmin can't be found, try:
/usr/bin/mysqladmin -u root password YourPassword