  Fundamental parameters are determined for three bright, nearby K-giants,
{\beta} Gem (K0 III), {\mu} Leo (K2 III), and {\alpha} Tau (K5 III). It is
notable that around all three stars the giant planets have been found. Our
results are compared with published high-precision data for benchmark stars
included in the Gaia project. Very good agreement was obtained for all three
giants with these data for the basic parameters Teff, logg, and M. Special
attention was devoted to analysis of the Fe I lines which are the basis of a
simultaneous determination of the metallicity index [Fe/H] and microturbulent
parameter Vt. The equivalent widths W of the Fe I lines are automatically
measured from published spectra for the benchmark stars. An analysis of Fe I
lines from the list of "golden lines" selected in a study of benchmark stars
led to the conclusion that the excitation potential El of the low level of the
lines plays an substantial role in determining [Fe/H] and Vt. It is shown that
in the case of the early K-giants {\beta} Gem and {\mu} Leo for lines in the
range of W from 100 to 300 m{\AA} there is a dependence of the [Fe/H] and Vt
values on El. It is shown that a correct accounting for it leads an ambiguity
in the determination of [Fe/H] and Vt for {\beta} Gem and {\mu} Leo. In the
case of the coolest K-giant {\alpha} Tau (Aldebaran) with a temperature Teff =
3920K, this effect seems to be less pronounced. Recommendations are given for
the Fe I lines selection for [Fe/H] and Vt determination. It is sonfirmed for
the example of the three stars studied here that the non-LTE effects in the Fe
I lines for the K-giants with normal metallicity are very minor, so they cannot
be the reason of the revealed ambiguity in [Fe/H] and Vt values. The low ratios
of the carbon 12C/13C and oxygen 16O/17O isotopes confirm that all three giants
passed the phase of deep convective mixing.
