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Location: Royal Palace Throne Room, King Helseth
Once you speak to Helseth, he'll ask that you prove yourself by fighting his champ, Karrod, in a duel. He's the silent Redguard standing next to Helseth. You're to come back tomorrow prepared, and prove your mettle. You can rest somewhere, or simply wait until the next morning or day. A reader provided this tip: if you go to the Winged Guar tavern after receiving this quest and speak with the bartender, he'll offer to make Karrod tired with one of his girls, so that for the fight the next day, Karrod's weaker.
When you're ready, speak to Helseth again, and choose to fight Karrod. Helseth will step back and Karrod will brandish his weapon. It's now time to fight. This can be a tough fight on max difficulty, so be prepared with magic enchantments and a lot of potions ready just in case. Once his damage is low enough (100 or less), Karrod will surrender to your greater skills. Now speak with Helseth. He'll reward you with the Dagger of Symmachus, one of the items the Museum of Artifacts is looking for. A second word of advice here. Keep this Dagger along with one other elite item the Museum is looking for. Do not sell them, as you'll need two artifacts for a later part of the main quest.
At this point, Helseth might ask you to find out more information about Almalexia. If he does not, come back later and speak with him again when you need something from Karrod. For now, Helseth's quests are finished, so go and visit Almalexia, because she'll have something for you to do.