What is the discriminant of a quadratic and why does it tell us the number of solutions?
1 Answer
See below:
Explanation:
I'd be glad to offer a little "primer" on discriminants of quadratics:
If we have the quadratic
We have three cases:
Why does this makes sense?
Recall the Quadratic Formula
What do you notice? The discriminant is the value under the radical.
If we want to think about how many solutions a quadratic has, the
Remember that if we take the square root of a negative number, we get imaginary values. So if
What happens when
When
Whatever is under the radical determines how many solutions we'll have.
I want to clarify that to determine the number of solutions, you don't have to plug the values into the Quadratic Formula. Plug in the values into the discriminant, and see what you get.
Hope this helps!