What are 2 integers whose product is -24 and whose sum is 6?

Answer 1

There are two numbers that meet those conditions, but they are not integers. You can work this out by taking the two statements and expressing them as equations, then using substitution to solve.

We're told that we have two numbers that add up to six and that multiply to make -24. If we call those numbers x and y, we can say:

x + y = 6

xy = -24

Now we'll take the first of them, and solve for y:

y = 6 - x

And substitute it into the latter:

x(6 - x) = -24

6x - x2 = -24

x2 - 6x - 24 = 0

We now have a quadratic equation and can solve it this way:

x2 - 6x - 24 = 0

x2 - 6x + 9 = 33

(x - 3)2 = 33

x - 3 = ±√33

x = 3 ± √33