Deep-rooted means the same as deep-seated. long-term solutions to a deep-rooted problem. a deep-rooted habit, idea, belief etc is so strong in a person or society that it is very difficult to change or destroy it deep-seated
(used especially of ideas or principles) deeply rooted; firmly fixed or held; "deep-rooted prejudice"; "deep-seated differences of opinion"; "implanted convictions"; "ingrained habits of a lifetime"; "a deeply planted need