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Math Help - x-intercepts with cubic

  1. #1
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    x-intercepts with cubic

    Hi all,

    Looking for some help to find if there is a "proper" way for doing this which I'm sure there is.

    This is the equation.

     x^3 - 3x + 5

    I'm doing lots of things to it like finding turning points etc etc, but I need to sketch it and show important points.

    To do this, I need to find the x-intercept.

    I really just don't know how to factorize this and get the correct answer. I know (via plugging into graphing calculator) that there is only one x intercept, and it's -2.27902. However I wish to do this 'properly' and learn how to find the factor on my own.

    Factorizing doesn't seem to help, because the usual solution I would do is this.

    x^3 - 3x = -5
    x^2 (x - 3) = -5
    x = +/- \sqrt{-5} (impossible for my purposes) or x = -2

    Any help as to the proper way to do this without trial and error would be appreciated.

    Cheers.
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  2. #2
    Member SENTINEL4's Avatar
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    Quote Originally Posted by Peleus View Post
    x^3 - 3x = -5
    x^2 (x - 3) = -5
    Your second line is wrong.. It is

    x^3 - 3x = -5
    x (x^2 - 3) = -5
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  3. #3
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    You need to rearrange equation to get x = cube root of (3x - 5)

    Then you use the iteration formula x(n+1) = cube root(3x(n) - 5)

    and it gives you x = -2.279018786 after a number of iterations
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  4. #4
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    Quote Originally Posted by SENTINEL4 View Post
    Your second line is wrong.. It is

    x^3 - 3x = -5
    x (x^2 - 3) = -5
    Woops, my silly mistake, I suppose the point still stands though because -5 and +/- root -2 aren't solutions.
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  5. #5
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    Quote Originally Posted by mathswend View Post
    You need to rearrange equation to get x = cube root of (3x - 5)

    Then you use the iteration formula x(n+1) = cube root(3x(n) - 5)

    and it gives you x = -2.279018786 after a number of iterations
    Cool, as far as my memory goes I've never heard of / seen the iteration formula, can you point me in the right direction for learning this? Simply google or if you can briefly explain it would be awesome.

    Thanks for your help.

    Edit - Or is it simply another name for trial and error?
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  6. #6
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    you simply rearrange your formula to get x =....

    in this case x = cube root(3x - 5)

    then you choose a starting point for x... say x = 1

    second value is cube root(3(1) - 5) = -1.25992105
    third value is cube root(3(-1.25992105) - 5) = -2.062976433
    fourth value is cube root(3(-2.062976433) - 5) = -2.236640458

    this keeps getting closer and closer to the root of the equation, so the more you do it the better your answer.

    Hope this helps.
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