Recently, it was observed that the roots of the Askey-Wilson polynomial are retrieved at the unique global minimum of an associated strictly convex Morse function [J. F. van Diejen and E. Emsiz, Lett. Math. Phys. 109 (2019), pp. 89-112]. The purpose of the present note is to infer that the corresponding gradient flow converges to the roots in question at an exponential rate.