The product of two numbers is 144 but their sum is-24 what are these two numbers?

The 2 numbers are 12 and12

The easiest way is to use the following quadratic equation related to sum and product:

X² - SX + P = 0, where S = sum and P = product

X² - (-24) X + 144 = 0

X² + 24X + 144 = 0.

Extract the roots: X' = [-b+√ (b²-4ac) ]/2a and X" = [-b-√ (b²-4ac) ]/2a

X' = [-24+√ (-24) ²-4 (1) (144) ]/2 X' = (-24√0) / 2 → X' = X" = - 12

Then the 2 numbers are - 12 and - 12