Question

Write two numbers that multiply to the value on top and add to the value on bottom.

27
-12

Answer 1

Multiply 3x9 and it gives u 27
And -3 plus -9 equal -12

Answer 2

-3 and -9

Explanation:

First, it is helpful to write out what is given by the question, with variables x and y.

x*y = 27

x+y = -12

Now we will isolate a variable from one and plug it into the other:

y = -12 - x

x(-12-x) = 27

-x^2 -12x -27 = 0

x^2 + 12x + 27

(x + 9) (x + 3) = 0

x must be either -9 or -3

Now we plug those x-values into either equation to get their corresponding y-values:

-9 + y = -12

y = -3

-3 + y = -12

y = -9

We can see that the first x value (-9) corresponds to y = -3, and the second pair is -3 and -9. Either way, the pair is -3 and -9.

Therefore the pair of numbers must be -3 and -9.