Who were the two Popes in the History of the Roman Catholic Church who spoke wrongly

this was given to me as a research homework, please help!

I don't know what you are talking about. By the power of the Holy Spirit, the Pope cannot fail in the teachings of the church. Mainly, because the doctrine of the Roman Catholic Church is the same as that of the teachings of the Apostles.

Catholic popes operated under the precept of infallibility when speaking about doctrine. They can not "speak wrongly". Since they are speaking God's words, to imply they are wrong means God is less than perfect.

Could that be Sregius III and John XII 904-964 commonly called "The Great Pornocracy".

Pope Nickolas and Lateran!

People mistakenly understand how papal infallibility works and that is why you get the answer none.

You are going to have a hard time finding that answer outside of an academic library. Pope's can and do speak incorrectly as do Ecumenical Councils, however, those times are not considered infallible.

The requirement for infallibility is that it is always believed, that it occurs in union with the bishops and that it is accepted by the laity. If any of these are not met, it is not an infallible statement.

I feel sorry for you on homework. There is also a context question. Any Christian can error in their personal discussions of faith and morals, so I suspect the list is longer than you think. What you are looking for are a narrow set of papal documents, under probably one thousand, in which a material error occur ed and which was intended to be a formal teaching.