Final answer:
Jocasta neglects to pursue King Laius' murderer because she does not believe in prophecies, citing that a prophecy about Laius' death was not fulfilled as stated. Creon avoids the investigation to maintain his position and avoid political instability in Thebes. Both characters' actions are ironically bound within the tragic fulfillment of the oracle’s prophecy.
Step-by-step explanation:
The question pertains to why Jocasta and Creon neglected to pursue King Laius' murderer in the play 'Oedipus Rex.' The answer to this lies primarily in the web of fate and prophecies that ensnare the characters. The oracle’s foretelling and the character's reactions, or lack thereof, to the prophecy play significant roles in shaping the events of the story.
In 'Oedipus Rex,' Jocasta and Creon have various reasons for not actively seeking the murderer of King Laius. Jocasta, in part, neglects the pursuit because she does not put much stock in prophecies, despite the oracle’s decree being the reason for the plague on Thebes. She firmly believes that prophecies are unreliable, citing the one about Laius being supposedly killed by his son, but knowing he was actually slain by bandits at a crossroad. This dismissal of prophecy leads her to discourage Oedipus from delving too deeply into matters which, in turn, is why she neglects to pursue her former husband's killer.
Creon, who is more political in his approach, does not push for an investigation into Laius’ murder, as it might destabilize his power and position within Thebes. He becomes king after the death of Oedipus and aims to maintain order during this turbulent period.
The complexity and ultimate tragedy of the story arise from a cruel twist of fate: in trying to evade a horrendous destiny, Oedipus unwittingly rushes towards it. Despite his and Jocasta's choices, they cannot outmaneuver the predetermined outcome set by the gods. This underlying theme of inescapable fate is central to the narrative and contributes to why Laius' murder is not pursued by Jocasta and Creon—their actions, or inactions, are all within the bounds of the prophecy’s fulfillment.