SOLUTION: m squared - 9m -24 ,Factor the type one qudratic

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Question 442276: m squared - 9m -24 ,Factor the type one qudratic
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
What multiplies to -24 and adds to -9?
Here are the factors of -24.
Plus or Minus here:
1 24
2 12
3 8
4 6
This cannot be factored in terms of integers.
Let's try the quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-9x%2B-24+=+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%2A1%2A-24=177.

Discriminant d=177 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+177+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+177+%29%29%2F2%5C1+=+11.152067347825
x%5B2%5D+=+%28-%28-9%29-sqrt%28+177+%29%29%2F2%5C1+=+-2.15206734782504

Quadratic expression 1x%5E2%2B-9x%2B-24 can be factored:
1x%5E2%2B-9x%2B-24+=+1%28x-11.152067347825%29%2A%28x--2.15206734782504%29
Again, the answer is: 11.152067347825, -2.15206734782504. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-9%2Ax%2B-24+%29


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