SOLUTION: find the x-intercepts of the graph of f(x)=4x^2-9x+4

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: find the x-intercepts of the graph of f(x)=4x^2-9x+4       Log On


   

Question 972297: find the x-intercepts of the graph of f(x)=4x^2-9x+4
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the x-intercepts of the graph of f(x)=4x^2-9x+4
--------------
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-9x%2B4+=+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=%28-9%29%5E2-4%2A4%2A4=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+17+%29%29%2F2%5C4+=+1.64038820320221
x%5B2%5D+=+%28-%28-9%29-sqrt%28+17+%29%29%2F2%5C4+=+0.609611796797792

Quadratic expression 4x%5E2%2B-9x%2B4 can be factored:
4x%5E2%2B-9x%2B4+=+%28x-1.64038820320221%29%2A%28x-0.609611796797792%29
Again, the answer is: 1.64038820320221, 0.609611796797792. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-9%2Ax%2B4+%29