Krax was the son of Grand Nagus Zek and the unofficial heir-apparent to the throne of the Ferengi Alliance. Krax was shocked when Zek unexpectedly nominated Quark to be his successor in 2369, and immediately retired. When Zek died shortly thereafter, Krax plotted with Quark's brother Rom to assassinate the new Nagus.
Fortunately for Quark, Zek reappeared a short time later, revealing that the entire incident had been a ruse to test Krax's eligibility for becoming the new Nagus. Krax failed the test miserably; as Zek said, "You don't grab power... you accumulate it, quietly." (DS9: "The Nagus")