  In this paper we present an algorithm to obtain the parameter planes of
families of root-finding methods with several free critical points. The
parameter planes show the joint behaviour of all critical points. This
algorithm avoids the inconsistencies arising from the relationship between the
different critical points as well as the indeterminacy caused by the square
roots involved in their computation.
  We analyse the suitability of this algorithm by drawing the parameter planes
of different Newton-like methods with two and three critical points. We also
present some results of the expressions of the Newton-like operators and their
derivatives in terms of palindromic polynomials, and we show how to obtain the
expression of the critical points of a Newton-like method with real
coefficients.
