Question

What multiplies to -12 but added together equals -10

Answer 1

Let the two numbers be x and y, then,
xy = -12 . . . (1)
x + y = -10 . . . (2)
From (2), x = -10 - y . . . (3)
Putting (3) into (1), gives
(-10 - y)y = -12
-10y - y^2 = -12
y^2 + 10y - 12 = 0

`y= (-10\pm √(10^2-(4*(-12))) )/(2) = (-10\pm √(148) )/(2) = (-10\pm 2√(37) )/(2) = -5\pm√(37)`

Therefore, the two numbers are
`-5+√(37)` and
`-5-√(37)`