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## Homework Statement

What is the condition, for a quadratic function of the form

ax

^{2}+ 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 = ax

^{2}+ 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?