  The power of the disconjugacy properties of second-order differential
equations of Schr\"odinger type to check the regularity of rationally-extended
quantum potentials connected with exceptional orthogonal polynomials is
illustrated by re-examining the extensions of the isotonic oscillator (or
radial oscillator) potential derived in kth-order supersymmetric quantum
mechanics or multistep Darboux-B\"acklund transformation method. The function
arising in the potential denominator is proved to be a polynomial with a
nonvanishing constant term, whose value is calculated by induction over k. The
sign of this term being the same as that of the already known highest-degree
term, the potential denominator has the same sign at both extremities of the
definition interval, a property that is shared by the seed eigenfunction used
in the potential construction. By virtue of disconjugacy, such a property
implies the nodeless character of both the eigenfunction and the resulting
potential.
