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April 19th, 2008, 07:16 AM
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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 | 
April 19th, 2008, 07:50 AM
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Originally Posted by ice_syncer 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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"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert | 
April 20th, 2008, 06:28 AM
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Originally Posted by topsquark | 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
-27a^2d+b^3 is the discriminant, funny part is, the discriminant is always 0 so the actual formula is -b/3a. 
Ice SYnc | 
April 20th, 2008, 06:38 AM
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Originally Posted by ice_syncer 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
-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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"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert | 
April 20th, 2008, 06:43 AM
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Originally Posted by topsquark 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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April 20th, 2008, 06:46 AM
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Originally Posted by ice_syncer 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 | 
April 20th, 2008, 08:34 AM
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Originally Posted by topsquark 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 | 
April 20th, 2008, 08:37 AM
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Originally Posted by mr fantastic 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 | 
April 20th, 2008, 09:16 AM
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Originally Posted by ice_syncer 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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April 20th, 2008, 09:37 AM
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Originally Posted by Isomorphism | Wait isnt due to Galois Theory that we know there cant be a quintic equation? | 
April 20th, 2008, 10:32 AM
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Originally Posted by Mathstud28 Wait isnt due to Galois Theory that we know there cant be a quintic equation? | Read this
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