This is a basic question but I can seem to explain it.

The Quadratic Equation term "b^2 -4ab" why do we change 

it to "b^2+ 4ab" when the "b" value is negative?

----------------------------------------------------

We don't. First of all it's not b²-4ab, it's b²-4ac. 

Also your example:

b^2-4ab (x^2-6x-27=0) = 6^2+4(1)(-27)=144 

is incorrect in the next to last step, although 144 is correct.

It should be

b^2-4ab (x^2-6x-27=0) = 6^2-4(1)(-27)=144 

What you have there, namely,

6^2+4(1)(-27)=

equals to -72, not 144.



Suppose we have

     2x² + 5x - 3

then a=2, b=5, and c=-3

So

     b² - 4ac

becomes

     (5)² - 4(2)(-3)

or

     25 - (-24)

and then the " - " sign before the parentheses and the " - "  

before the 24 inside the parentheses becomes a " + ", and we

have

    25 + 24

or

    49 



Edwin 

 

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