bespeak vs quest

bespeak is not a noun while quest is a noun.

Word	Noun	Adjective	Verb	Adverb
bespeak	No	No	Yes	No
quest	Yes	No	Yes	No

As verbs, bespeak and quest are synonyms defined as:

Other synonyms of bespeak include ask for, call for, request.

bespeak (noun)	quest (noun)
	the act of searching for something
	a search for an alternative that meets cognitive criteria

bespeak (verb)	quest (verb)
express the need or desire for	seek alms, as for religious purposes
be a signal for or a symptom of	express the need or desire for
	bark with prolonged noises, of dogs
	search the trail of (game)
	make a search (for)