SOLUTION: -4x^2+14x-6=0 solve for the zeros

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: -4x^2+14x-6=0 solve for the zeros      Log On


   

Question 693596: -4x^2+14x-6=0 solve for the zeros
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
+-4x%5E2%2B14x-6=0+
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4x%5E2%2B14x%2B-6+=+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=%2814%29%5E2-4%2A-4%2A-6=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-14%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2814%29%2Bsqrt%28+100+%29%29%2F2%5C-4+=+0.5
x%5B2%5D+=+%28-%2814%29-sqrt%28+100+%29%29%2F2%5C-4+=+3

Quadratic expression -4x%5E2%2B14x%2B-6 can be factored:
-4x%5E2%2B14x%2B-6+=+-4%28x-0.5%29%2A%28x-3%29
Again, the answer is: 0.5, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B14%2Ax%2B-6+%29