# 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

*vertex* of the quadratic!

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]}