Porque crees que lo conquistadores romanos utilizaban el latin como lengua de adminstracion

The Romans were implementing the Latin language as the language of the administration for both, practical reasons and also assimilation of the native population they have managed to conquer.

By making the local chieftains learn, speak, and use the Latin language, the Romans played very well tactically, because in this way the leaders of the tribes were slowly becoming assimilated into the Roman culture, and once the local leaders are assimilated it has a chain reaction and the people that are under their guidance are starting to assimilate as well.