Question 257949: They give me this example:x squared -8x-20=0
(x-10)(x+2)=0
x-10=0 or x+2=0
x=10 or x=-2
I do not understand were they get -10 and +2. Why not 5 and 4. Also why is the 2 positive.
Answer by Greenfinch(383)   (Show Source):
You can put this solution on YOUR website! 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
|
|
|
