SOLUTION: What is a way that we can tell how many solutions we will have by something from the quadratic formula?

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Question 161521: What is a way that we can tell how many solutions we will have by something from the quadratic formula?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is a way that we can tell how many solutions we will have by something from the quadratic formula?
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The discriminant shows that.
Take any example:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A1%2A2=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+-1
x%5B2%5D+=+%28-%283%29-sqrt%28+1+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B3x%2B2 can be factored:
1x%5E2%2B3x%2B2+=+%28x--1%29%2A%28x--2%29
Again, the answer is: -1, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B2+%29

The onsite solver explains it well