Generalizations of Hensel's lemma and the nearest root method

Hensel's lemma and its various modifications, such as, for instance, the Hensel–Rychlik theorem, are important tools for investigating problems of existence of roots of polynomials in valued fields. It is shown that a method proposed in the author's previous papers can also be used to provide a simpler derivation of results by S. Khanduja in [J. Pure Appl. Algebra, 214, No. 12 (2010), 2294–2300].