1. The problem statement, all variables and given/known data What is the condition, for a quadratic function of the form ax2 + bx + c = y to be a perfect square? (x, y are real here) There's a question of this type in a book I'm working with, and I'd just like to have some general conditions for any quadratic... 3. The attempt at a solution Since y = ax2 + bx + c = a(x-[tex]\alpha[/tex])(x-[tex]\beta[/tex]) where [tex]\alpha[/tex] and [tex]\beta[/tex] are the values of x for which y = 0, y is a perfect square when Discriminant of quadratic = 0 (this ensures that [tex]\alpha[/tex] = [tex]\beta[/tex]) and when a is a perect square.. Are these the required conditions for any quadratic function (of the given form) to be a perfect square? Any condition I may have missed?