word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
"sure to have the desired effect" (often of medicines), 1520s, from Latin efficaci-, stem of efficax "powerful, effectual, efficient," from stem of efficere "work out, accomplish" (see effect (n.)) + -ous. Related: Efficaciously; efficaciousness.
<a href="https://www.etymonline.com/word/inefficacious">Etymology of inefficacious by etymonline</a>
Harper, D. (n.d.). Etymology of inefficacious. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inefficacious