SOLUTION: This problem I must factor the quadratic expression completely, and find the roots of the expression. 6x^2 - 42x + 72

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: This problem I must factor the quadratic expression completely, and find the roots of the expression. 6x^2 - 42x + 72      Log On


   

Question 234938: This problem I must factor the quadratic expression completely, and find the roots of the expression.

6x^2 - 42x + 72
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 6x%5E2%2B-42x%2B72+=+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=%28-42%29%5E2-4%2A6%2A72=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--42%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-42%29%2Bsqrt%28+36+%29%29%2F2%5C6+=+4
x%5B2%5D+=+%28-%28-42%29-sqrt%28+36+%29%29%2F2%5C6+=+3

Quadratic expression 6x%5E2%2B-42x%2B72 can be factored:
6x%5E2%2B-42x%2B72+=+%28x-4%29%2A%28x-3%29
Again, the answer is: 4, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-42%2Ax%2B72+%29