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Math Help - Positive root solution

  1. #1
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    Positive root solution

    Hi, I've been given the following question for homework.
    Determine if the following characteristic equation represents a stable or unstable system.

    s^3+6s^2+11s+6=0

    Any tips in solving this would be of great help.
    Thanks
    Last edited by mr fantastic; May 23rd 2009 at 03:01 AM. Reason: Fixed the close latex tag.
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  2. #2
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    Hi there

    Quote Originally Posted by ady72 View Post
    Hi, I've been given the following question for homework.
    Determine if the following characteristic equation represents a stable or unstable system.

    s^3+6s^2+11s+6=0

    Any tips in solving this would be of great help.
    Thanks
    I found one zero by guessing, it is s=-1. (I know, this is very disappointing, but very fast compared with other methods like http://en.wikipedia.org/wiki/Newton%27s_method or http://en.wikipedia.org/wiki/Cubic_f...ano.27s_method)

    Using polynomial long division leads to

    (s^3+6s^2+11s+6)/(s-(-1))

    = s^2 + 5s + 6

    You should be able to find the other two zeros, -3 and -2

    All zeros are < 0, therfor I guess (but I don't know) it represents a stable system.

    Cheers
    Rapha
    Last edited by mr fantastic; May 23rd 2009 at 03:02 AM.
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  3. #3
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    Thanks Rapha, that has helped meno end.
    Cheers
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