Zeta Corporation, a multinational conglomerate, is evaluating the carrying value of its long-lived assets for potential impairment. As part of its annual assessment, Zeta Corporation identifies an asset group with a carrying value of $5,000,000 and an estimated undiscounted cash flow of $4,500,000.

In light of this discovery, determine whether an impairment loss needs to be recognized for the asset group, and if so, calculate the amount of impairment loss to be recorded. Provide a comprehensive explanation of the impairment testing process and its implications for Zeta Corporation's financial statements and disclosures.