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...
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?