Who Was Solomon's Father? David's Oath in 1 Kings 1
Solomon's father was David, king of Israel, and 1 Kings 1 makes the point twice over: David calls Solomon his son and then publicly sets him on the throne. The chapter answers the family question and the succession question together.
Who Was Solomon's Mother? 2 Samuel 12:24
Solomon's mother was Bathsheba, and 2 Samuel 12:24 names her plainly as David's wife. The verse does not tidy the story; it sets the future king's birth inside the aftermath of sin, confession, and loss, then rests its weight on God's love for the child.