The nation of Israel themselves is not sure if there really was a King David. If you want a factual answer to your question, then you have to wait until the existence of King David is established; or...
David was the son of Jesse of Bethlehem:-
1Sa 16:1 And the LORD said unto Samuel, How long wilt thou mourn for Saul, seeing I have rejected him from reigning over Israel? fill thine horn with oil,...
#1.
He was the king of Judea in which was the old name of the country of Israel where Bethlehem and Jerusalem were situated. David reigned over all Israel. The time that he reigned over Israel was...