Two numbers multiply to be 24 and add to be -11. What are the numbers?

Answer 1

Let the numbers be represented by x and y.

Then:

xy = 24

x+y = -11

From the 2nd equation y = -x-11 (substitute into the 1st equation)

x(-x-11) = 24

-x²-11x=24

x²+11x+24=0

(x+8)(x+3) = 0

So:

x+8 = 0 or x+3=0

x = -8 or x = -3

y = -3 y = -8

Check:

(-3)(-8) = 24

(-3)+(-8) = -11