Thread: 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

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

Originally Posted by topsquark

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

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


Ice SYnc

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

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

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

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

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

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

Originally Posted by Isomorphism

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?

Originally Posted by Mathstud28

Wait isnt due to Galois Theory that we know there cant be a quintic equation?

Read this