In "Beowulf," what does Beowulf's speech to King Hrothgar reveal about his personality?
Beowulf is somewhat boastful when he first arrives at Hrothgar's hall. He says that news of their plight with Grendel has reached his land and so he's come to fight Grendel. He tells of his victories in battles against both human and non-human foes (monsters). He goes on to say that he hopes Hrothgar will allow him, with the help of his men, to purge Hrothgar's land of the evil Grendel. He promises to be victorious or die trying. This tells us that Beowulf is very confident in himself and his abilities. It also tells us that he has a very high opinion of his abilities. He says that he doesn't plan to use any weapons because that would be unfair since Grendel doesn't use any weapons. This is more boasting on Beowulf's part, but it also tells us he has a strong sense of fairness. He finishes his opening speech to Hrothgar by saying that fate must play out as it is designed to play out. This tells us that Beowulf believes in fate and predestination. He is alluding to the idea that he was fated to fight Grendel and win.
In his speech, Beowulf gives his ancestry and how he heard about Grendel. He also tells us why he came to help--that Hrothgar helped Beowulf's father in his time of need, and now out of sense of honor and duty to Hrothgar, Beowulf returns the favor. He also tells why he is the man for the job. Later, he tells Hrothgar's party that he killed nine sea monsters while swimming with Brecca in the sea.
So, from his speech, we learn that he is confident, bold, brave, loyal, perhaps a bit boastful (but remember that the Anglo-Saxons didn't necessarily believe in an after-life...they believed that the only way to "live forever" was to perform amazing feats that people would tell stories about forever), and strong.
It goes without saying that he is welcomed and believed...the party Hrothgar threw for him in preparation for Beowulf's encounter with Grendel is proof enough of their confidence in him.