Bash completion can be enabled in the file .bashrc as explained in this Q&A. In your case it seems to be correct in your user's .bashrc, but not in your root's .bashrc. The latter file is located in /root/.bashrc. Open this file with your favorite text editor as root (e.g. by running sudo gedit /root/.bashrc) and remove the # in the beginning of the last three lines:

You have to change the lines 98-100 from

#if [ -f /etc/bash_completion ] && ! shopt -oq posix; then

#    . /etc/bash_completion

#fi

...to:

if [ -f /etc/bash_completion ] && ! shopt -oq posix; then

    . /etc/bash_completion

fi

Then close your terminals and reopen them.