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