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Math Help - solve inequality equation

  1. #1
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    Post solve inequality equation

    Solve inequality equation:

    x^2-5x-6<0
    Last edited by mr fantastic; February 23rd 2011 at 03:33 AM. Reason: Copied title into main body of post.
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  2. #2
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    This is easiest to solve by completing the square.
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    Quote Originally Posted by hoanghai549 View Post
    Solve inequality equation:

    x^2-5x-6<0
    Draw a graph of y = x^2 - 5x - 6 and clearly label the x-intercepts. For what values of x is y < 0 ....?
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    Quote Originally Posted by mr fantastic View Post
    Draw a graph of y = x^2 - 5x - 6 and clearly label the x-intercepts. For what values of x is y < 0 ....?
    Perhaps it's a way as long as you have a quadratic, but how about a higher degree polynomial? Even worse, you're giving an exam and there's nothing no graph it faster, there's where analytically way comes handy.
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    Quote Originally Posted by hoanghai549 View Post
    Solve inequality equation:

    x^2-5x-6<0
    An algebraic solution is

    x^2-5x-6<0\Rightarrow\ (x-6)(x+1)<0

    This is negative if the product of the factors gives (-)(+)

    If x<-1, both factors are negative

    and if x>6, both factors are positive, hence in both cases the product will be positive.

    Therefore, one can find from this the valid range of x.

    Alternatively

    x^2-5x-6<0\Rightarrow\ x^2-5x<6\Rightarrow\ x(x-5)<6

    x>6\Rightarrow\ (+)(+)>6

    x<-1\Rightarrow\ (-)(-)>6

    Again, the range of x can be deduced.
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