We characterize the ability of the ALHAMBRA survey to assign accurate photo-zs to BLAGN and QSOs based on their ALHAMBRA very-low-resolution optical-NIR spectroscopy. A sample of 170 spectroscopically identified BLAGN and QSOs have been used together with a library of templates (including SEDs from AGN, normal, starburst galaxies and stars) in order to fit the 23 photometric data points provided by ALHAMBRA in the optical and NIR (20 medium-band optical filters plus the standard JHKs). We find that the ALHAMBRA photometry is able to provide an accurate photo-z and spectral classification for ~88% of the spectroscopic sources over 2.5 deg^2 in different areas of the survey, all of them brighter than m678=23.5 (equivalent to r(SLOAN)~24.0). The derived photo-z accuracy is better than 1% and comparable to the most recent results in other cosmological fields. The fraction of outliers (~12%) is mainly caused by the larger photometric errors for the faintest sources and the intrinsic variability of the BLAGN/QSO population. A small fraction of outliers may have an incorrectly assigned spectroscopic redshift. The definition of the ALHAMBRA survey in terms of the number of filters, filter properties, area coverage and depth is able to provide photometric redshifts for BLAGN/QSOs with a precision similar to any previous survey that makes use of medium-band optical photometry. In agreement with previous literature results, our analysis also reveals that, in the 0<z<4 redshift interval, very accurate photo-z can be obtained without the use of near-IR broadband photometry at the expense of a slight increase of outliers. The NIR importance is expected to increase at higher redshifts (z>4). These results are relevant for the design of future optical follow-ups of surveys with a large fraction of BLAGN, as it is the case for X-rays or radio surveys.
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