Problem with User and password now requested

[PiEmme]

On a Linux server a MySql db is installed.
I was able to run mysql and mysqladmin without entering user and
password, at first.
Later both user and password have become required. Probably after
granting root user to two different php applications accessing db's
(applA, dbA, user=root, pwd=pwdA; applB, dbB, user=root, pwd=pwdB).
Now all db's have user=root with password=uniquePwd.

How can I reset, and have user and pwd no more requested?

The main problem now is that a cron job fails, because unable to
access mysql, as in the following report:

running daily cronjob scripts

SCRIPT: clean_catman, OK.
SCRIPT: clean_core, OK.
SCRIPT: do_mandb, OK.
SCRIPT: logrotate exited with RETURNCODE = 1.
SCRIPT: ouput (stdout && stderr) follows

/usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Access denied for user: 'root@localhost' (Using password: NO)'
error running postrotate script
Reload syslog service..done
SCRIPT: logrotate
------- END OF OUTPUT

Thank you.