RU-ALLRUSSIAN 1983 Problem 10

Given a quadratic equation $\mathrm{ax}^2 +\mathrm{bx} + \mathrm{c}$ . If it has two real roots $\mathrm{A}\leq \mathrm{B}$ , transform the equation to $\mathrm{x}^2 +\mathrm{Ax} + \mathrm{B}$ . Show that if we repeat this process we must eventually reach an equation with complex roots. What is the maximum possible number of transformations before we reach such an equation?