  We point out that in general the Reissner-Nordstr\"om (RN) charged black
holes of general relativity are not solutions of the four dimensional quadratic
gravitational theories. They are, e.g., exact solutions of the $R+R^2$
quadratic theory but not of a theory where a $R_{ab}R^{ab}$ term is present in
the gravitational Lagrangian. In the case where such a non linear 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 $Q\ll M$ the
validity of this solution extends down to the horizon. This allows us to
explore the thermodynamic properties of the quadratic charged black hole and we
find that, to our approximation, its thermodynamics is identical to that of a
RN black hole. However our black hole's entropy is not equal to the one fourth
of the horizon area. Finally we extend our analysis to the rotating charged
black hole and qualitatively similar results are obtained.
