Let us assume the two numbers to be "x" and "y".
Then
xy = - 24
x = - (24/y)
And
x + y = 2
Putting the value of x from the first equation in the second equation, we get
x + y = 2
- (24/y) + y = 2
- 24 + y^2 = 2y
y^2 - 2y - 24 = 0
y^2 - 6y + 4y - 24 = 0
y(y - 6) + 4(y - 6) = 0
(y - 6) (y + 4) = 0
When
y - 6 = 0
y = 6
Then
x + y = 2
x + 6 = 2
x = 2 - 6
= -4
And when
y + 4 = 0
y = -4
Then
x + y = 2
x - 4 = 2
x = 2 + 4
= 6
So the two unknown numbers are -4 and 6.
