We present optical spectroscopy of a sample of 38 post-starburst quasars (PSQs) at z ~ 0.3, 29 of which have morphological classifications based on Hubble Space Telescope imaging. These broad-lined active galactic nuclei (AGNs) possess the spectral signatures of massive intermediate-aged stellar populations making them potentially useful for studying connections between nuclear activity and host galaxy evolution. We model the spectra in order to determine the ages and masses of the host stellar populations, and the black hole masses and Eddington fractions of the AGNs. Our model components include an instantaneous starburst, a power-law, and emission lines. We find the PSQs have MBH ~ 10^8 Msun accreting at a few percent of Eddington luminosity and host ~ 10^10.5 Msun stellar populations which are several hundred Myr to a few Gyr old. We investigate relationships among these derived properties, spectral properties, and morphologies. We find that PSQs hosted in spiral galaxies have significantly weaker AGN luminosities, older starburst ages, and narrow emission-line ratios diagnostic of ongoing star-formation when compared to their early-type counterparts. We conclude that the early-type PSQs are likely the result of major mergers and were likely luminous infrared galaxies in the past, while spiral PSQs with more complex star-formation histories are triggered by less dramatic events (e.g., harassment, bars). We provide diagnostics to distinguish the early-type and spiral hosts when high spatial resolution imaging is not available.
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