Etymology
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inquest (n.)
Origin and meaning of inquest
late 13c., enquest, an-queste "legal or judicial inquiry," especially one before a jury, from Old French enqueste "inquiry" (Modern French enquête), from Vulgar Latin *inquaestia (source also of Italian inchiesta), from Latin inquisita (res) "(a thing) looked into; an inquiry," from fem. past participle of Latin inquirere "to seek after, search for" (see inquire). The form with in- prevailed from 18c.
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quest (n.)

c. 1300, "an inquest, a judicial inquiry;" early 14c., "a search for something, the act of seeking, pursuit" (especially in reference to hounds seeking game in the hunt), from Old French queste "search, quest, chase, hunt, pursuit; inquest, inquiry" (12c., Modern French quête), properly "the act of seeking," and directly from Medieval Latin questa "search, inquiry," alteration of Latin quaesitus (fem. quaesita) "sought-out, select," past participle of quaerere "seek, gain, ask" (see query (n.)).

The medieval romance sense of "adventure undertaken by a knight" (especially the search for the Grail) is attested from late 14c. Chaucer has questmonger (late 14c.), "one who profits from an unjust action at law."

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jury (n.)

"set number of persons, selected according to law and sworn to determine the facts and truth of a case or charge submitted to them and render a verdict," early 14c. (late 12c. in Anglo-Latin), from Anglo-French and Old French juree (13c.), from Medieval Latin iurata "an oath, a judicial inquest, sworn body of men," noun use of fem. past participle of Latin iurare "to swear," from ius (genitive iuris) "law, an oath" (see jurist).

Meaning "body of persons chosen to award prizes at an exhibition" is from 1851. Grand jury attested from early 15c. in Anglo-French (le graund Jurre), literally "large," so called with reference to the number of its members (usually 12 to 23). Jury-box is from 1729; juryman from 1570s. Figurative phrase jury is still out "no decision has been made" is by 1903.

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question (n.)

early 13c., questioun, "philosophical or theological problem" (especially when phrased as an interrogative statement), early 14c. as "utterance meant to elicit an answer or discussion," also as "a difficulty, a doubt," from Anglo-French questiun, Old French question "question, difficulty, problem; legal inquest, interrogation, torture," and directly from Latin quaestionem (nominative quaestio) "a seeking, a questioning, inquiry, examining, judicial investigation," noun of action from past-participle stem of quaerere "ask, seek" (see query (v.)).

Also in Middle English "verbal contention, debate; legal proceedings, litigation, accusation." Phrase a question of meaning "a dispute about" is from early 15c.

No question "undoubtedly" is from mid-15c; no questions asked "accountability not required" is from 1879 (especially in newspaper advertisements seeking the return of something lost or stolen). To be out of the question (c. 1700) is to be not pertinent to the subject, hence "not to be considered." To be in question "under discussion or consideration" is from 1610s.

Question mark is from 1849, sometimes also question stop (1862), earlier interrogation point (1590s). The figurative sense of "something about which there is uncertainty or doubt" is from 1869.  

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