SOLUTION: Please Find the exact solutions to 3x^2 = 5x - 1 by using the quadratic formula.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Please Find the exact solutions to 3x^2 = 5x - 1 by using the quadratic formula.      Log On


   

Question 294310: Please Find the exact solutions to 3x^2 = 5x - 1 by using the quadratic formula.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2 - 5x +1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%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=%28-5%29%5E2-4%2A3%2A1=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+13+%29%29%2F2%5C3+=+1.43425854591066
x%5B2%5D+=+%28-%28-5%29-sqrt%28+13+%29%29%2F2%5C3+=+0.232408120756002

Quadratic expression 3x%5E2%2B-5x%2B1 can be factored:
3x%5E2%2B-5x%2B1+=+3%28x-1.43425854591066%29%2A%28x-0.232408120756002%29
Again, the answer is: 1.43425854591066, 0.232408120756002. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-5%2Ax%2B1+%29