equation problem

Hedgecutter

Hi, I was doing calculus turning points of a curve in evening class last night and this happened in the middle of a problem.

the teacher described the method as the big X.
could anyone explain it for me.

Things were moving very fast last night and meant to ask after class. Think its simple enough but would like an explanation.

Iancar29

Basically , what you have on the left is the factors of X^2 ( X and X )

What you have on the right hand side is the factors of -6 that when added give you the number in front of the x in the middle , which is -1 .

So then ( x-3) = 0 and (x+2) = 0
solving for x we get then

x = 3 and x = -2


SO heres another example


X^2 -12x - 32


So drawing your "big X " again you'll have on left X and X

and on the right hand side you want the factors of -32 , that when added give -12

So in this case its -8 and -4 .

Then its ( x - 8 )(x- 4) = 0

solving for X , x = 8 x = 4

Alot of people including myself never actually liked using the "BIG X" , and just went straight to putting down your brackets with the x on each side then whatever factors then of the constant that gives the middle number.


But yeah , hope that helps

Hedgecutter

Iancar29 wrote: »

Basically , what you have on the left is the factors of X^2 ( X and X )

What you have on the right hand side is the factors of -6 that when added give you the number in front of the x in the middle , which is -1 .

So then ( x-3) = 0 and (x+2) = 0
solving for x we get then

x = 3 and x = -2


SO heres another example


X^2 -12x - 32


So drawing your "big X " again you'll have on left X and X

and on the right hand side you want the factors of -32 , that when added give -12

So in this case its -8 and -4 .

Then its ( x - 8 )(x- 4) = 0

solving for X , x = 8 x = 4

Alot of people including myself never actually liked using the "BIG X" , and just went straight to putting down your brackets with the x on each side then whatever factors then of the constant that gives the middle number.


But yeah , hope that helps

Big help cheers, I understand now. Thanks.

Blackpanther95

Why any teacher explains how to solve quadratics like that I don't know. When solving quadratics just remember if you have
(x+a)(x+b) then the term before the x is got by adding a to b and the constant(no x's or x^2's) is got by multiplying, obviously, just think about it. I have to multiply everything in the first bracket by everything in the second, so the only way to get a constant is to multiply the to last etc (guessing is by far the best way to solve this easily) so the equation is x^2+(a+b)x+ab .