Update MySQL root password in Ubuntu 14.04

Edit /etc/mysql/my.cnf, and add the following line

 skip-grant-tables

Restart MySQL service

 $ sudo service mysql restart

Login to mysql and modify passwords

 $ mysql -u root
 mysql> UPDATE mysql.user set password = PASSWORD('YOUR NEW PASSWORD') where user = 'root' and host = 'localhost';
 mysql> quit

Restart MySQL service

 $ sudo service mysql restart

You should be able to login to MySQL with your new password

 $ mysql -u root -p