SOLUTION: What are the approximate values of x that are solutions to f(x)=0 where f(x)= -2x^2+3x+9

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Question 918822: What are the approximate values of x that are solutions to f(x)=0 where
f(x)= -2x^2+3x+9
Answer by asuar010(338) 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%2B3x%2B9+=+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=%283%29%5E2-4%2A-2%2A9=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+81+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+81+%29%29%2F2%5C-2+=+-1.5
x%5B2%5D+=+%28-%283%29-sqrt%28+81+%29%29%2F2%5C-2+=+3

Quadratic expression -2x%5E2%2B3x%2B9 can be factored:
-2x%5E2%2B3x%2B9+=+-2%28x--1.5%29%2A%28x-3%29
Again, the answer is: -1.5, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B3%2Ax%2B9+%29