>>>which can have none, 1 or 2 solutions, depending on a, b, c. (In fact, if we're looking for a complex solution, there is always at least one.)
>>>
>>Re: ax**2 + bx + c = 0, standard form.
>
>I wrote: aX^2+bX+c=0. It's exactly the same thing. :) It's just a different notation.
>
>>And I might add, for applied solutions you might just want to do a "Discriminant" check, if b**2 - 4*a*c < 0, there are no real solutions, only an imaginary pair.
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>So, where's the difference between what I said and this one? The number of solutions in complex?
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>Any real number is also a complex one. (The set of complex numbers includes the set of real numbers). So, if you're looking for solutions in complex, you can have 1 or 2 solutions. If there's only one (the discriminant = 0), you're right, the solution has only real part. But that doesn't mean is not a complex one.
>
Quite right, R is a subset of C, C is form a +/- bi where a,b are real, i=sqrt(-1), and b=0 for R (real), etc.
I'm only saying that in the real world, you usually don't want non-real solutions, so we do a discriminant check before we proceed any further. If data can't pass this test, we throw it out and/or go back to check it for errors, depending on the situation...

Maybe we need new category, 'mathematics stuff' :~)