SOLUTION: 4x^2-4x+1=0 I need to calculate the discriminant and how many real solution it has.

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 4x%5E2%2B-4x%2B1+=+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

:

.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-4%29%29%2F2%5C4

.
Expression can be factored: 4x%5E2%2B-4x%2B1+=+4%28x-0.5%29%2A%28x-0.5%29

Again, the answer is: 0.5, 0.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-4%2Ax%2B1+%29