Etymology
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deep-seated (adj.)

1741, "having its root far below the surface," hence "firmly implanted," from deep (adv.) + past participle of seat (v.). Figurative use is by 1847. Deep-rooted is from early 15c.

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Definitions of deep-seated

deep-seated (adj.)
(used especially of ideas or principles) deeply rooted; firmly fixed or held;
deep-seated differences of opinion
Synonyms: deep-rooted / implanted / ingrained / planted
From wordnet.princeton.edu