SOLUTION: factor the algebraic expressions completely 6x^2 - 28x + 16

Algebra ->  Expressions -> SOLUTION: factor the algebraic expressions completely 6x^2 - 28x + 16      Log On


   

Question 35386: factor the algebraic expressions completely
6x^2 - 28x + 16
Answer by lyra(94) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-28x%2B16+=+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=%28-28%29%5E2-4%2A6%2A16=400.

Discriminant d=400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--28%2B-sqrt%28+400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-28%29%2Bsqrt%28+400+%29%29%2F2%5C6+=+4
x%5B2%5D+=+%28-%28-28%29-sqrt%28+400+%29%29%2F2%5C6+=+0.666666666666667

Quadratic expression 6x%5E2%2B-28x%2B16 can be factored:
6x%5E2%2B-28x%2B16+=+6%28x-4%29%2A%28x-0.666666666666667%29
Again, the answer is: 4, 0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-28%2Ax%2B16+%29


Hope this helps,
lyra