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We show a double path mechanism for the formation of charged excitons (trions); they are formed through bi- and trimolecular processes. This directly implies that both negatively and positively charged excitons coexist in a quantum well, even in the absence of excess carriers. The model is substantiated by time-resolved photoluminescence experiments performed on a very high quality InxGa1-xAs quantum well sample, in which the photoluminescence contributions at the energy of the trion and exciton and at the band edge can be clearly separated and traced over a broad range of times and densities. The unresolved discrepancy between the theoretical and experimental radiative decay time of the exciton in a doped semiconductor quantum well is explained by the same model.