SOLUTION: solve this problem..... f(x)=2x^2+24x using the quadratic formula

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Question 866079: solve this problem.....
f(x)=2x^2+24x using the quadratic formula
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+2x%5E2%2B24x%29+
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B24x%2B0+=+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=%2824%29%5E2-4%2A2%2A0=576.

Discriminant d=576 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-24%2B-sqrt%28+576+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2824%29%2Bsqrt%28+576+%29%29%2F2%5C2+=+0
x%5B2%5D+=+%28-%2824%29-sqrt%28+576+%29%29%2F2%5C2+=+-12

Quadratic expression 2x%5E2%2B24x%2B0 can be factored:
2x%5E2%2B24x%2B0+=+2%28x-0%29%2A%28x--12%29
Again, the answer is: 0, -12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B24%2Ax%2B0+%29