# Can Mathematica find the discriminant formula? [duplicate]

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?

• The command 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, 2014 at 21:07
• You don't understand. Imagine that I have ax^2 + bx + c = 0, but we do not know about discriminant (people didn't invent it yet :)) ). Than we'll solve it like this scienceforums.net/topic/3798-proof-of-the-discriminant . By multiplying and adding to equation symbols to make part of equation look like square of sum, so we can solve that equation. Can mathematica act like that? Change equation so it look like one of mathematica pattern. In other words, can one reinvent descriminant solution with mathematica? :))) Mar 30, 2014 at 21:21
• Consider how you might go about solving for a double root in your generic quadratic equation. (Set derivative to zero...) Mar 31, 2014 at 3:04