Final answer:
The technician should inform the student that the broken radiator neck is a serious issue that needs immediate attention. It can cause coolant leakage, engine overheating, and potential engine damage. Replacing the radiator neck is necessary to fix the problem.
Step-by-step explanation:
When the technician tells you that the neck on the radiator has broken off during a coolant flush, it means that the part of the radiator where the coolant is filled has snapped off. This is a serious issue as it can lead to coolant leakage, overheating of the engine, and possible engine damage. The radiator neck will need to be replaced in order to fix the problem and prevent further damage to the vehicle.