SOLUTION: What two numbers times together make -15 but when sum together make -3

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Question 1051984: What two numbers times together make -15 but when sum together make -3
Found 2 solutions by Alan3354, jorel555:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What two numbers times together make -15 but when sum together make -3
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If you mean the product is -15, and the sum is -3:
x*y = -15
x + y = -3
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y = -3 - x
x*(-3-x) = -15
x%5E2+%2B+3x+-+15+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-15+=+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%2A1%2A-15=69.

Discriminant d=69 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+69+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+69+%29%29%2F2%5C1+=+2.65331193145904
x%5B2%5D+=+%28-%283%29-sqrt%28+69+%29%29%2F2%5C1+=+-5.65331193145904

Quadratic expression 1x%5E2%2B3x%2B-15 can be factored:
1x%5E2%2B3x%2B-15+=+%28x-2.65331193145904%29%2A%28x--5.65331193145904%29
Again, the answer is: 2.65331193145904, -5.65331193145904. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-15+%29

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The 2 solutions are the 2 numbers.

Answer by jorel555(1290) About Me  (Show Source):
You can put this solution on YOUR website!
Let m and n be your numbers. Then:
m+n=-3
mn=-15
So:
n-m=3
n=3+m
m(3+m)=-15
mē+3m+15=0
Using the quadratic formula, we get m= -1.5 + 3.57071421427i, and n=
-1.5 - 3.57071421427i. ☺☺☺☺