SOLUTION: This problem I must factor the quadratic expression completely, and find the roots of the expression. 135x^2 - 222x + 91

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: This problem I must factor the quadratic expression completely, and find the roots of the expression. 135x^2 - 222x + 91      Log On


   

Question 234937: This problem I must factor the quadratic expression completely, and find the roots of the expression.
135x^2 - 222x + 91
Answer by philline_palana(20) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 135x%5E2%2B-222x%2B91+=+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=%28-222%29%5E2-4%2A135%2A91=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--222%2B-sqrt%28+144+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-222%29%2Bsqrt%28+144+%29%29%2F2%5C135+=+0.866666666666667
x%5B2%5D+=+%28-%28-222%29-sqrt%28+144+%29%29%2F2%5C135+=+0.777777777777778

Quadratic expression 135x%5E2%2B-222x%2B91 can be factored:
135x%5E2%2B-222x%2B91+=+%28x-0.866666666666667%29%2A%28x-0.777777777777778%29
Again, the answer is: 0.866666666666667, 0.777777777777778. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+135%2Ax%5E2%2B-222%2Ax%2B91+%29