For which values of the parameter $a$ does the equation \[(2x-a)\sqrt{ax^2-(a^2+a+2)x+2(a+1)}=0\]has three different real roots.
Problem
Source: 2008 Bulgarian Autumn Math Competition, Problem 10.1
Tags: Real Roots, algebra, parameter
Source: 2008 Bulgarian Autumn Math Competition, Problem 10.1
Tags: Real Roots, algebra, parameter
For which values of the parameter $a$ does the equation \[(2x-a)\sqrt{ax^2-(a^2+a+2)x+2(a+1)}=0\]has three different real roots.