SOLUTION: Why are there usually two solutions in quadratic equations

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Question 171610: Why are there usually two solutions in quadratic equations
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
In a simple parabola such as y=x^2
You have two x answers for y. It can be positive x or negative x.
x can equal +1 or -1 to get y=1
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B0+=+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=%280%29%5E2-4%2A1%2A0=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%280%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B0x%2B0+=+1%28x-0%29%2A%28x-0%29

Again, the answer is: 0, 0. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B0+%29


I hope that this helps.