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Thread: Roots of a 3rd degree polynomial

  1. #1 Roots of a 3rd degree polynomial 
    Forum Sophomore Stranger's Avatar
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    Hi,

    I think I heard of formulae that directly get you the roots of a degree 3 polynomial. I mean, like the ones of a degree 2 which are

    (-b + or - (b^2 - 4 ac)^1/2) / 2a

    I'm posting this question because I need them like that, in symbols. I don't care about the numerical value since I can get it using my calculator.

    Thanks very much.


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  3. #2  
    Forum Professor river_rat's Avatar
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    The formula is not pretty - dpmms does the whole derivation thing which is always a good place to start

    http://www.dpmms.cam.ac.uk/~wtg10/cubic.html


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  4. #3  
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    The formula is not pretty at all! I cannot work with that one.

    I guess I will try to find a different approach...

    Thanks for the link.
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  5. #4  
    Forum Isotope Zelos's Avatar
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    pretty? all formulas are pretty. They are just less or more simple
    I am zelos. Destroyer of planets, exterminator of life, conquerer of worlds. I have come to rule this uiniverse. And there is nothing u pathetic biengs can do to stop me

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  6. #5  
    Forum Sophomore Stranger's Avatar
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    Simplicity is beautiful, complexity interesting. Personal opinion.
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  7. #6  
    Forum Isotope Zelos's Avatar
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    Logic is beautiful
    Therefor correct math is beutifull
    Therefor is physics beutifull
    I am zelos. Destroyer of planets, exterminator of life, conquerer of worlds. I have come to rule this uiniverse. And there is nothing u pathetic biengs can do to stop me

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  8. #7  
    Forum Professor river_rat's Avatar
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    Quote Originally Posted by Stranger
    The formula is not pretty at all! I cannot work with that one.

    I guess I will try to find a different approach...

    Thanks for the link.
    Well you formula's for everything up to the quartic and if you limit yourself to only taking roots then thats were you stop (Galois Theory 101) though an asymptotic expansion for a cubic with small leading co-efficient is usually suffient for most physcial applications. Why do you want a formula?
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  9. #8  
    Forum Professor river_rat's Avatar
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    Quote Originally Posted by Zelos
    pretty? all formulas are pretty. They are just less or more simple
    Lol - ive seen some really ugly formula before, just start expaning Einsteins field equations in simple cartesian co-ordinates with out any symmetry considerations!
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  10. #9  
    Forum Freshman .:Elusive.Neutrino:.'s Avatar
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    Zelos is just being a smartass. :P
    <i8b4uUnderground> d-_-b
    <BonyNoMore> how u make that inverted b?
    <BonyNoMore> wait
    <BonyNoMore> never mind
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  11. #10  
    Forum Isotope Zelos's Avatar
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    all hail zelos
    I am zelos. Destroyer of planets, exterminator of life, conquerer of worlds. I have come to rule this uiniverse. And there is nothing u pathetic biengs can do to stop me

    On the eighth day Zelos said: 'Let there be darkness,' and the light was never again seen.

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  12. #11  
    Forum Sophomore Absane's Avatar
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    If you guys think the solution to the cubic is not pretty, has anyone seen the solution to the quartic? Degree 4? That's insane. So insane I forgot it.
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  13. #12  
    Forum Sophomore Elbethil's Avatar
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    Quote Originally Posted by Absane
    If you guys think the solution to the cubic is not pretty, has anyone seen the solution to the quartic? Degree 4? That's insane. So insane I forgot it.
    The Quartic Formula

    From that same page, lol:
    The formulas for the roots are much too unwieldy to be used for solving quartic equations by radicals, even with the help of a computer.
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  14. #13  
    Forum Sophomore Absane's Avatar
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    Quote Originally Posted by Elbethil
    Quote Originally Posted by Absane
    If you guys think the solution to the cubic is not pretty, has anyone seen the solution to the quartic? Degree 4? That's insane. So insane I forgot it.
    The Quartic Formula

    From that same page, lol:
    The formulas for the roots are much too unwieldy to be used for solving quartic equations by radicals, even with the help of a computer.
    I don't know.. that seems like a lot more than I had to do. I just remember having to solve these by hand last year

    And I thought the cubic was enough work...
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