SOLUTION: Determine the break-even points of the profit function P(x)= -2x^2+7x+8, where x is the number of dirt bikes produced, in thousands.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Determine the break-even points of the profit function P(x)= -2x^2+7x+8, where x is the number of dirt bikes produced, in thousands.      Log On


   

Question 914357: Determine the break-even points of the profit function P(x)= -2x^2+7x+8, where x is the number of dirt bikes produced, in thousands.
Answer by ewatrrr(24785) 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 -2x%5E2%2B7x%2B8+=+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%2A-2%2A8=113.

Discriminant d=113 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+113+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+113+%29%29%2F2%5C-2+=+-0.907536453183662
x%5B2%5D+=+%28-%287%29-sqrt%28+113+%29%29%2F2%5C-2+=+4.40753645318366

Quadratic expression -2x%5E2%2B7x%2B8 can be factored:
-2x%5E2%2B7x%2B8+=+-2%28x--0.907536453183662%29%2A%28x-4.40753645318366%29
Again, the answer is: -0.907536453183662, 4.40753645318366. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B7%2Ax%2B8+%29