This is a great question. Let me give you a few answers.
First, David left an indelible mark on Judaism and Christianity in many different ways. For example, his faith, his writing (Psalms), and his example of courage. However, the great way in which David impacted Christians and Jews is through the covenant God made with him in 2 Samuel 7. This covenant basically stated that God would raise up a davidic line, which would usher in the ultimate king. For Christians, this is Christ. This is why the gospels seek to show that Jesus is from the line of David. Here are the words of 2 Samuel 7:11-13:
The Lord declares to you that the Lord himself will establish a house for you: When your days are over and you rest with your ancestors, I will raise up your offspring to succeed you, your own flesh and blood, and I will establish his kingdom. He is the one who will build a house for my Name, and I will establish the throne of his kingdom forever.
Second, when it comes to Solomon, this impact is more negative. Solomon will go down in history as the one whose heart became unfaithful towards the end of his reign to the point where God divided the kingdom on account of his divided heart. We read of this is 1 Kings 11:9-11:
The Lord became angry with Solomon because his heart had turned away from the Lord, the God of Israel, who had appeared to him twice. Although he had forbidden Solomon to follow other gods, Solomon did not keep theLord’s command. So the Lord said to Solomon, “Since this is your attitude and you have not kept my covenant and my decrees, which I commanded you, I will most certainly tear the kingdom away from you and give it to one of your subordinates.