When you system is configured to use DHCP.
/etc/resolv.conf file will be regenerated on each system boot via /sbin/dhclient-script.
However one would prefer to use Public DNS Servers instead the ones provided by the DHCP server.
According to dhclient-script man page, we can change the behavior by overeating the add_new_resolv_conf function in /etc/dhclient-enter-hooks file.
Now we can safely edit /etc/resolv.conf file - all changes will be persistent across system reboots.