Question 257949
x^2 - 8x - 20 = 0
ends up in the form (x + a)(x + b) = 0
which when expanded becomes x^2 + (a + b)x + (a x b) = 0
So a+b = -8 and a x b = -20
Either a or b is negative (but not both) since a x b is minus.
So a + b is the difference in the quantities (since one is negative)
If |a x b| is 20, a and b can be 1,20 : 2,10: 4,5.
the differences are then 19, 8 and 1
We need the 8 and since the 8 is minus, the numbers we need are -10 and +2 giving a sum of -8,
So the factors are (x - 10)(x + 2) = 0
Giving the roots  x = 10 or -2