Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted in the stride-piano tradition of Willie (The Lion) Smith and Duke Ellington, yet in many ways he stood apart from the mainstream jazz repertory.
(A) Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted
According to parallelism, if we use a verb after “both” we need to use a verb after “and”.
Both - rooted - (verb), and- Duke Ellington (noun)
If we were to use both, we could use it before Wille Smith.
In that case, the sentence would be- TM produced a body of works rotted in the stride-piano tradition of both Willie Smith and Duke Ellington.
“both” and “and” are followed by nouns in that case.
Eliminate.
(B) Thelonious Monk, the jazz pianist and composer, produced a body of work that was rooted both
Rooted both
- in the stride-piano tradition of Willie (The Lion) Smith
- Duke Ellington
This breaks parallelism. Eliminate.
(C) Jazz pianist and composer Thelonious Monk, who produced a body of work rooted
Jazz pianist and composer, TM, who (modifier)…, yet in many ways he …
“who” introduces a relative clause. There is no main verb in the sentence. Eliminate.
(D) Jazz pianist and composer Thelonious Monk produced a body of work that was rooted
Correct
(E) Jazz pianist and composer Thelonious Monk produced a body of work rooted both
Same as B. Eliminate