A class of new (we believe) third‐order formulae for the iterative solution of the equationf(x) =0 are derived. The formulae contain the methods of Chebyshev and Halley as special cases, and some numerical examples are given to demonstrate the convergence behaviour. General formulae of at least fourth‐order are also presented and, in particular, their application to the extraction of roots is illustrated. Apart from the potential for further investigations the study could be used as the theme of a student project on iterative methods for the solution off(x) = 0.