By the way, an aircraft that won't trim and rolls?!! Wouldn't fancy learning in that..
A lot of light aircraft can only be trimmed in pitch, not in roll or yaw. If there is a weight imbalance left/right, for instance due to fuel mismanagement (PA28) or because you're flying solo while the aircraft is rigged for dual, or because of general wear and tear of the airframe, or dirt on the wings, whatever, it will display a slight tendency to roll.
Ideally this is countered with aileron but that quickly gets tedious, particularly if you need your hands free for some other tasks. The other technique is to counter it with a tiny bit of rudder. This will lead to the aircraft flying slightly out of balance, so it'll be less efficient, but at least you've got your hands free, and a steady aircraft, to attend to other tasks.
On the other hand, a lot of student don't even get the pitch trim right, so they need to fly hands-on all the time anyway, and won't even notice the roll forces because of the higher pitch forces required to keep the aircraft level.