What can the discriminant be used for?

Question

What can the discriminant (b² – 4ac) be used for? Is it something to do with the number of solutions a quadratic equation has? Or something to do with roots? Please help, I have a presentation to make on it...

Answer 1

it can be used to determine HOW MANY SOLUTIONS a problem has.

When you use the discriminate, if the answer is negative there are no solutions

if it is 0 there is one solution

if it is positive there are two solutions

Answer 2

The discriminant determines whether there are two real roots of a quadratic equation, or just one real root, or two complex roots. If the discriminant is positive, two real roots. If it's zero, one real root (actually we say it's a repeated root, ie the same root twice!). And if the discriminant is negative, there are two 'complex' roots. Complex numbers are not done until precalculus though, so if you haven't done them yet, you can just say that in this case there are no real roots.
The graph of a quadratic equation is like a pudding bowl shape, going off to infinity. (That's if the x squared term is positive - if it's negative, it's an upside down pudding bowl).
If the disciminant is positive, there are two real roots, and these occur where the pudding bowl cuts the x axis.
If it is zero, the pudding bowl just sits on the x axis, and the place where it touches it, or sits, is the single (repeated) real root.
If it is negative, the pudding bowl floats above the x axis, and doesn't cut the axis or touch it anywhere - so there are no real roots.
Wish I could draw the pictures so you could use it in your project. Try and find them in an Algebra II book?
Good luck!

By the way, by a 'pudding bowl' I mean a salad bowl maybe, or the rounded basin shape of a lake.

Answer 3

This discriminant (other things are called discriminants, too) tells you whether the solutions to a quadratic equation are real, imaginary or both zero. This term has application in electricity and in structural analysis.

Answer 4

yes, disriminant is used to determine how many solutions a quadratic has

if b^2 - 4ac > 0, there are two solutions
if b^2 - 4ac = 0, there is one solutions
if b^2 - 4ad < 0, there are no solutions

Answer 5

In addition to what Darkgem said..

Dont forget..Anytime that you are working a quadratic eqution..Like in Physics say..The formulat is -b+-sqrt(b^2-4ac)/2a can be a VERY convienent way of solving some of the more difficult problems..Without factoring or completing the square.

Answer 6

If it is a positive number it will have two real roots.
If it is negative it will have two imaginary roots, no real ones.
If it is 0 then there will be one real root.