Final answer:
Rome defeated the forces of the Greek warrior-king Pyrrhus two generations prior to Virgil's birth, leading to its eventual control over Italy.
Step-by-step explanation:
The rival state that Rome defeated two generations prior to Virgil's birth was the Greek warrior-king Pyrrhus's forces. Around 280 BCE, Pyrrhus, who had already established control over parts of Greece, was invited by Greek colonies in southern Italy to aid them against the Romans. Despite winning two major battles, the costs were so high for Pyrrhus's army that they had to withdraw, leading to the eventual Roman control of all Italy by 263 BCE. This term is also where the phrase "pyrrhic victory" originates, indicating a victory that comes at such a great cost that it is tantamount to defeat.