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    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.
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    sketch a graph
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    (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 ?
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    (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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