# Thread: Discriminant of Roots - Stucked @ part ii after completing part i

1. 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 ? $\displaystyle ax^2 + bx + c$.

2. Originally Posted by Bacterius
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 ? $\displaystyle ax^2 + bx + c$.
Yes totally agree with you but I am not trying to complicate things up heh, just trying to find the fault of my mistake, checking if the fault lies in the way I express the equation

3. Don't worry, once you will have fully grasped the theory behind quadratic equations and practiced a lot, it will become a reflex and you will be unbeatable on them

4. Guess the art of getting an A1 in E-Maths and A-Maths is Practise, I don't do well because I am a lazy bum...

5. 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

6. Thanks and I know about it

7. However, one question,

is it true that to prove that an equation intercepts a curve, I have to equate the 2 equations and prove that it's discriminant has real roots?

8. In general, to prove that two curves modeled by two equations $\displaystyle F(x)$ and $\displaystyle G(x)$ intercept, you have to prove that the equation $\displaystyle F(x) = G(x)$ admits at least one solution for $\displaystyle x$.

9. Originally Posted by punch
However, one question,

is it true that to prove that an equation intercepts a curve, I have to equate the 2 equations and prove that it's discriminant has real roots?
do you mean: show that y= x intersects the parabola y = x^2 in two points

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

10. 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.

11. If the 2 lines(Curve and the line) intercepts, it means that the roots are real...
Not at all ! It means that for one or more $\displaystyle x$, they share a same $\displaystyle y$.

The discriminant needn't be used in every single problem you meet, sometimes it's easier to leave it alone and solve without it.

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