Question

Product -12 and sum -1 what are the factors

Answer 1

the two numbers are 3 and -4

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.