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Math Help - Find out expression of a cubic function

  1. #1
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    Exclamation Find out expression of a cubic function

    i have a question i have no idea how to solve.....


    Find an expression for a cubic
    function f if f(3) = 54 and f(-3) = f(0) = f(4) = 0.

    f(x) =_________________________


    Does anyone know how to solve this.
    Last edited by mr fantastic; September 20th 2009 at 04:52 PM. Reason: Removed excessive ! from post title, changed last line of post to lower case
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  2. #2
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    Quote Originally Posted by Sneaky View Post
    i have a question i have no idea how to solve.....


    Find an expression for a cubic
    function f if f(3) = 54 and f(-3) = f(0) = f(4) = 0.

    f(x) =_________________________


    Does anyone know how to solve this.
    Since you have three roots you can start by using the model y = a (x - \alpha) (x - \beta) (x - \gamma) where x = \alpha, \, \beta and \gamma are the known roots of the cubic.

    Then substitute f(3) = 54 and solve for a.
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  3. #3
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    Quote Originally Posted by Sneaky View Post
    i have a question i have no idea how to solve.....


    Find an expression for a cubic
    function f if f(3) = 54 and f(-3) = f(0) = f(4) = 0.

    f(x) =_________________________


    Does anyone know how to solve this.
    they gave you the zeros ...

    f(x) = kx(x+3)(x-4) , where k is some constant

    and you know f(3) = 54 ... you can find out what k is
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