By default, mysql does not allow remote login to the root user. Remote login error 1045 can easily cause the illusion that the password is incorrect. To achieve this, additional authorization is required.
Log in to the root user of mysql locally and enter the following command (the * in the middle is the password):
GRANT ALL PRIVILEGES ON *.* TO 'root'@'%' IDENTIFIED BY '******' WITH GRANT OPTION;
FLUSH PRIVILEGES;