RU-ALLRUSSIAN 1971 Problem 6

The real numbers a, b, A, B satisfy $(\mathrm{B} - \mathrm{b})^{2}< (\mathrm{A} - \mathrm{a})(\mathrm{Ba} - \mathrm{Ab})$ . Show that the quadratics $\mathrm{x}^{2}+$ $\mathrm{ax} + \mathrm{b} = 0$ and $\mathrm{x}^{2} + \mathrm{Ax} + \mathrm{B} = 0$ have real roots and between the roots of each there is a root of the other.