A seeking undertaken deliberately and at cost. What separates a quest from a search is that the seeker is changed by it.
Old French queste (a search, a seeking), from Vulgar Latin quaesta, from Latin quaerere (to seek, to ask); a quest was named for the seeking itself, and only later for the trial that seeking becomes.
A seeking undertaken deliberately and at some cost. What separates a quest from a plain search is that the root's seeking changes the seeker along the way, which a search never promises to do.