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Math Help - Polynomial inequalities

  1. #1
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    Polynomial inequalities

    Solve the inequality:

    y^3 - 6y^2 + 8y < 0

    So here is what I did, just following the steps to follow a normal equation

    y (y - 6y + 8) < 0
    y (y - 2) (y - 4) < 0

    So what are the answers and how do i express them?
    Last edited by Power; June 18th 2008 at 06:28 PM.
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    See here.
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  3. #3
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    Thanks but I dont get all that stuff, with the infinity signs and stuff. Is there a easier method?
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  4. #4
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by Power View Post
    Solve the inequality:

    y^3 - 6y + 8y < 0

    So here is what I did, just following the steps to follow a normal equation

    y (y - 6y + 8) < 0
    y (y - 2) (y - 4) < 0

    So what are the answers and how do i express them?
    A product is negative iff it has an odd number of negative term(s). In this case, there are three terms. ( y, y-2 and y-4) As the only odd numbers in \{1,2,3\} are 1 and 3, the product is negative if one term is negative or if the three are negative. Does it help ?
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  5. #5
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    Quote Originally Posted by flyingsquirrel View Post
    Hi


    A product is negative iff it has an odd number of negative term(s). In this case, there are three terms. ( y, y-2 and y-4) As the only odd numbers in \{1,2,3\} are 1 and 3, the product is negative if one term is negative or if the three are negative. Does it help ?
    So whats the solution? I mean a solution expressed without a graph.
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  6. #6
    Math Engineering Student
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    I suggest you to take another look to my link provided, it's the best way to tackle your problem, besides it's faster.
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