SOLUTION: f(x)= 3x-2/x+7

Algebra ->  Functions -> SOLUTION: f(x)= 3x-2/x+7      Log On


   

Question 284195: f(x)= 3x-2/x+7
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
3x -2/x + 7 = 0
.
Multiply by x to remove denominator.
.
x(3x -2/x + 7) = x(0)
3x^2 -2 +7x = 0
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B7x%2B-2+=+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=%287%29%5E2-4%2A3%2A-2=73.

Discriminant d=73 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+73+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+73+%29%29%2F2%5C3+=+0.257333957552922
x%5B2%5D+=+%28-%287%29-sqrt%28+73+%29%29%2F2%5C3+=+-2.59066729088625

Quadratic expression 3x%5E2%2B7x%2B-2 can be factored:
3x%5E2%2B7x%2B-2+=+3%28x-0.257333957552922%29%2A%28x--2.59066729088625%29
Again, the answer is: 0.257333957552922, -2.59066729088625. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B7%2Ax%2B-2+%29