This question is not really practical, but rather a curiosity question.
Can Mathematica solve a quadratic equation without its discriminant?
I mean, whenever it see a quadratic equation it tries to solve it with discriminant. (I use Trace for that)
But could it find it discriminant formula by itself?
I mean, the discriminant was found by human, and looking from how it was found, I see that was not very easy.
I know that Mathematica looks for patterns in equations. Can it found patterns, like discriminant?
Discriminant(see the documentation) does what you want. Of course you can also re-invent that function yourself. Do want exactly the same functionality? – Jens Mar 30 '14 at 21:07