Product - 12 and sum - 1 what are the factors

the two numbers are 3 and - 4

Step-by-step explanation:

Product: xy = - 12, or x = - 12/y

Sum: x + y = - 1, or - 12/y + y = - 1

Let's multiply all three terms by y to eliminate the fractional terms:

-12 + y^2 = - y, or

y^2 + y - 12 = 0

This factors into (y + 4) (y - 3) = 0, yielding y = - 4 and y = 3.

Earlier we found that x = - 12/y. Here, if we choose y = - 4, x = - 12 / (-4) = 3

and so the two numbers are 3 and - 4. Note that 3 (-4) = - 12, as required, and that 3 - 4 = - 1, also as required.