How do you find the discriminant for #3x^2-x=8# and determine the number and type of solutions?
1 Answer
There are 2 real number solutions:
Explanation:
Using the discriminant, we can evaluate the type and number of roots to a quadratic using these rules (explanation comes after):
- if
#Delta=0# then there is 1 root - if
#Delta>0# then there are 2 real number roots - if
#Delta<0# then there are 2 complex roots
Note that
But why?
Well, let's take a look at the quadratic formula:
We are going to focus on this term here:
It's quite obvious that if
It should also be a bit obvious that if
as there is no real number such that that number squared gives a negative, using the wonderful language of Math:
If
Regarding the number of roots, we can see that the term
When
Wow! The two roots and the vertex is one point!! Let me leave you off with this pretty example of the discriminant equal to
graph{x^2-4x+4 [-10, 10, -5, 5]}