We point out that in general the Reissner-Nordstrom (RN) charged black
holes of general relactivity are not solutions of the four-dimensiona
l quadratic gravitational theories. They are, e.g., exact solutions of
the R + R2 quadratic theory but not of a theory where a R(ab)R(ab) te
rm is present in the gravitational Lagrangian. In the case where such
a nonlinear curvature term is present with sufficiently small coupling
we obtain an approximate solution for a charged black hole of charge
Q and mass M. For Q much less than M the validity of this solution ext
ends down to the horizon. This allows us to explore the thermodynamic
properties of the quadratic charged black hole and we find that, to ou
r approximation, its thermodynamics is identical to that of a RN black
hole. However our black hole's entropy is not equal to one-fourth of
the horizon area. Finally we extend our analysis to the rotating charg
ed black hole and qualitatively similar results are obtained.