I'm not sure what your asking here, but the quadratic discriminant is [itex]\Delta = b^2 - 4ac[/itex]. The two roots areIs the discriminant, of the quadratic equations, the difference between the two roots?
Or is it a special case?
Yes Hooteny .I'm not sure what your asking here, but the quadratic discriminant is [itex]\Delta = b^2 - 4ac[/itex]. The two roots are
[tex]x_\pm = \frac{-b\pm\sqrt{\Delta}}{2a},[/tex]
with the difference being
[tex]x_+ - x_- = \frac{-b + \sqrt{\Delta} + b +\sqrt{\Delta}}{2a} = \frac{\sqrt{\Delta}}{a}.[/tex]
So in general, the discriminant is not the difference between the two roots. The condition for the discriminant to be the difference between the two roots is
[tex]\Delta = \frac{\sqrt{\Delta}}{a}\text{ or } \Delta = 0\;, \Delta = a^{-2}.[/tex]
The first corresponds to the case when you have repeated roots (obviously) and the second occurs when [itex]a^2b^2 - 4a^3c - 1 = 0[/itex].