Question

What number times what number equals 99 but has the sum of -34

Answer 1

Let the two numbers be x and y, then
xy = 99 . . . (1)
x + y = -34 . . . (2)
From (2), x = -34 - y . . . (3)
Putting (3) into (1), gives
(-34 - y)y = 99
-34y - y^2 = 99
y^2 + 34y + 99 = 0

`y= (-34\pm √(34^2-(4*99)) )/(2) = (-34\pm √(760) )/(2) = (-34\pm 2√(190) )/(2) = -17\pm√(190)`

Therefore, the two numbers are
`-17+√(190)` and
`-17-√(190)`