Question 41
Let the equation $x^2 + (a+b-1)x + ab - a - b = 0$, where $a$ and $b$ are positive integers such that $0 \lt a \leq b$.
a) Show that the equation has two distinct real solutions.
b) Prove that if one solution of the equation is an integer, then both solutions are non-positive integers and $b \lt 2a$.
a) Show that the equation has two distinct real solutions.
b) Prove that if one solution of the equation is an integer, then both solutions are non-positive integers and $b \lt 2a$.