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Math Help - Derive the Cubic formula

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    Derive the Cubic formula

    Hi, well, I tried deriving the cubic formula using solving the cube method but the cx and bx^2 seems to be a nuisance.

    Ice Sync
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ice_syncer View Post
    Hi, well, I tried deriving the cubic formula using solving the cube method but the cx and bx^2 seems to be a nuisance.

    Ice Sync
    If you are serious about this, try Cardano's method.

    -Dan
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    Quote Originally Posted by topsquark View Post
    If you are serious about this, try Cardano's method.

    -Dan
    Yeah well, I saw read that article before I posted it,
    anyways I did derive a formula by "completing the cube" method, just took 5 minutes, sadly it only works for perfect cubes or cubic equations with one root.

    It is [-b+ CUBEROOT(-27a^2d+b^3)]/3a

    -27a^2d+b^3 is the discriminant, funny part is, the discriminant is always 0 so the actual formula is -b/3a.


    Ice SYnc
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ice_syncer View Post
    Yeah well, I saw read that article before I posted it,
    anyways I did derive a formula by "completing the cube" method, just took 5 minutes, sadly it only works for perfect cubes or cubic equations with one root.

    It is [-b+ CUBEROOT(-27a^2d+b^3)]/3a

    -27a^2d+b^3 is the discriminant, funny part is, the discriminant is always 0 so the actual formula is -b/3a.


    Ice SYnc
    There are occasionally neat formulas that work for specific kinds of cubics, but solving one in general is rather difficult. And if you think cubics are bad, you should try quartics!

    -Dan
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    Quote Originally Posted by topsquark View Post
    There are occasionally neat formulas that work for specific kinds of cubics, but solving one in general is rather difficult. And if you think cubics are bad, you should try quartics!

    -Dan
    And if you want to contemplate the impossible, try quintics
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    Quote Originally Posted by ice_syncer View Post
    Hi, well, I tried deriving the cubic formula using solving the cube method but the cx and bx^2 seems to be a nuisance.

    Ice Sync
    Cubic function - Wikipedia, the free encyclopedia

    That is the general case....that would be nearly impossible to solve for...Wow

    just one root generally would be x=---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- that long basically
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    Quote Originally Posted by topsquark View Post
    There are occasionally neat formulas that work for specific kinds of cubics, but solving one in general is rather difficult. And if you think cubics are bad, you should try quartics!

    -Dan
    OK, forget the formulas, here's the best, use remainder theorem and reduce it to a quadratic equation , the use the quadratic formula!!


    Ice SYnc
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    Quote Originally Posted by mr fantastic View Post
    And if you want to contemplate the impossible, try quintics
    How about n-thics ( degree as n )

    wow , then we'd get a universal formula for solving any equation, forget it, use the remainder theorem
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    Quote Originally Posted by ice_syncer View Post
    How about n-thics ( degree as n )

    wow , then we'd get a universal formula for solving any equation, forget it, use the remainder theorem
    Well, no "n-thics" can yield a formula in terms of its coefficients for n > 4 by Abels Impossibility theorem. Try this link Abel's Impossibility Theorem -- from Wolfram MathWorld
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    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Isomorphism View Post
    Well, no "n-thics" can yield a formula in terms of its coefficients for n > 4 by Abels Impossibility theorem. Try this link Abel's Impossibility Theorem -- from Wolfram MathWorld
    Wait isnt due to Galois Theory that we know there cant be a quintic equation?
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  11. #11
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    Quote Originally Posted by Mathstud28 View Post
    Wait isnt due to Galois Theory that we know there cant be a quintic equation?
    Read this
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