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# Inequalities watch

1. I'm having some problems understanding quadratic inequalities, as I can solve the equations but then get stuck.

eg.

x^2-x+12>0
(x-4)(x+3)>0

and I get stuck on whether to do -3<x<4 or x<-3 or x>4
how do you decide on which one to use.
2. sketch a graph
3. (Original post by berwick53)
I'm having some problems understanding quadratic inequalities, as I can solve the equations but then get stuck.

eg.

x^2-x+12>0
(x-4)(x+3)>0

and I get stuck on whether to do -3<x<4 or x<-3 or x>4
how do you decide on which one to use.
y = (x-4)(x+3) is a U shaped parabola.

Sketch it marking where it crosses the x axis.

For which x values are the y values > 0 ?
4. (Original post by berwick53)
I'm having some problems understanding quadratic inequalities, as I can solve the equations but then get stuck.

eg.

x^2-x+12>0
(x-4)(x+3)>0

and I get stuck on whether to do -3<x<4 or x<-3 or x>4
how do you decide on which one to use.
well if they product is positive, both terms must be either >0 or <0
hence
x-4>0 and x+3>0 or x-4<0 and x+3<0
so
x>4 and x>-3 or x<4 and x<-3
since x must fulfill both x>4 and x>-3, x>4
since x must fufill both x<4 and x<-3, x<-3
hence x>4 or x<-3

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