Did you check whether the mysql user has the sufficient privilege to use mysqldump ? ie, if you log in as 'dolphin', but the mysql user is 'whale', then you need to use "mysqldump -uwhale -ppassword general > general.sql"
btw, your script above says 'mysqladmin' - I assume that's a typo ? Try this php shell script and see (it works on my system)
------- snip ------
#!/usr/local/bin/php -q
<?php
system("/path/to/mysqldump -p<password> general > general.db", $t);
echo "$t\n";
?>
Remember to chmod 755 the script first.
cheers.