Humans are more efficient when working with positive values (I personally hate having an equation with lots of plus and minus signs bundled up). And again, why complicate things ? $\displaystyle ax^2 + bx + c$.
Punch, you probably know this already, but if you don't (and to make things clearer):
when $\displaystyle b^2 - 4ac < 0, $there are no real roots. This means that the curve does not cut the x axis.
when $\displaystyle b^2 - 4ac >0 $, there are two distinct real roots. this means that the curve cuts the x axis twice (at two different points)
when $\displaystyle b^2 - 4ac =0, $ there is one real root. This means that the curve touches!
b^2 - 4ac is known as the discriminant.
also, I suggest you spend an hour or so reading about the concepts behind quadratics. a lot of these questions stem from understanding, rather than rote learning/memorising answers
do you mean: show that y= x intersects the parabola y = x^2 in two pointsOriginally Posted by punch
x = x^2
x^2 - x = 0
x(x-1) = 0
x = 0, x = 1
since there are two solutions for x, the curve y= x and y=x^2 intersect at two points
in some cases, you do not have to take the discriminant if it is easier to solve
I think I understand about the concept now.... If the 2 lines(Curve and the line) intercepts, it means that the roots are real...
Therefore, if the discriminant is more than or equals to zero, it shows that it has real roots and it intercepts.. However if the discriminant is <0, it shows that it has no real roots and therefore will NOT intercept...
Thanks everyone, more or less, I understand what a discriminant is now.
Not at all ! It means that for one or more $\displaystyle x$, they share a same $\displaystyle y$.If the 2 lines(Curve and the line) intercepts, it means that the roots are real...
The discriminant needn't be used in every single problem you meet, sometimes it's easier to leave it alone and solve without it.