Final answer:
In the play 'Oedipus Rex', Oedipus's biological parents are King Laius and Queen Jocasta of Thebes.
Step-by-step explanation:
The real parents of Oedipus in the play Oedipus Rex are Laius and Jocasta. Laius was the King of Thebes before Oedipus, and Jocasta was both Oedipus's mother and, later in the play, his wife, due to a series of tragic misunderstandings and the unfolding of fate as prophesied by the oracle of Delphi. This tragic discovery is pivotal in the conclusion of Sophocles's play, where Oedipus accepts responsibility for his actions, although they were prophesied and inadvertently carried out, ultimately leading to his downfall.