Clarification of a footnote of "On the generalized Nyquist stability criterion"

Prof. E.A. Francis pointed out to the original authors that footnote 31 on p. 189 of the above-named article [ibid., vol. AC-25, pp. 181-196, April 1980]. The footnote stated (incorrectly) that the discriminant could only be zero at a finite number of points in C. This is false. A correct reasoning is presented.