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A co workier of mine was asking about how this formaula was come up with. I could work it backwards to the Ax^2 + Bx + c =0, but when trying to go the other way, I could not explain where the number 4 comes from? Is it from "completeing the square"? or what?
I learnt this in grade 10. Its just a bunch of transformations. I'll dig it up and post it later.
As it turns out, my grade 10 math teacher wasnt the only one who knew.
http://mathforum.org/library/drmath/view/53153.html
and here http://library.thinkquest.org/29292/...lving/3derive/
ax2 + bx + c = 0
x2 + bx/a + c/a = 0
x2 + bx/a = -c/a
x2 + bx/a + b2/4a2 = b2/4a2 - c/a
Bolded term makes left side a perfect square.
(x + b/2a)2 = b2/4a2 - 4ac/4a2
x + b/2a = SquareRoot( b2/4a2 - 4ac/4a2 )
x + b/2a = SquareRoot( b2 - 4ac)/2a
x = -b/2a + SquareRoot( b2 - 4ac)/2a
The above is close enough to the standard formula.
You may want to mention that the b2/4a2 comes from completing the square.:)