SOLUTION: PLEASE SOLVE using quadratic formulas 3x2 -4x+1=0

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Question 27644: PLEASE SOLVE using quadratic formulas 3x2 -4x+1=0
Answer by askmemath(368) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you mean 3X%5E2+-4x+%2B1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%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: b%5E2-4ac=%28-4%29%5E2-4%2A3%2A1=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+4+%29%29%2F2%5C3+=+1
x%5B2%5D+=+%28-%28-4%29-sqrt%28+4+%29%29%2F2%5C3+=+0.333333333333333

Quadratic expression 3x%5E2%2B-4x%2B1 can be factored:
3x%5E2%2B-4x%2B1+=+3%28x-1%29%2A%28x-0.333333333333333%29
Again, the answer is: 1, 0.333333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B1+%29