Upon checking the script that you are using, the code belows in the script that says
mysqld_safe -user=mysql &
should start mysqld server as the user(mysql) "AND" should execute the
mysql_secure_installation script which will help you step through the following:
- Reset mysql root password
- Remove anonymous user
- Disable remote access to mysql
- Reload privilege tables.
- etc . .
And as what DavidPostill said above there is no default root password, so when it ask you to enter the default root password just hit "Enter".