MathNet 1971 — Part 01 Question 10

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