Thread: Help with quartic and quintics

Hey guys

Few days ago my teacher taught us about solving equations with degrees higher than 2, like x^3+2X^2+5X+12 or higher with x to the 4th of 5th. I can't help but get annoyed with synthetic division and long division, anybody know a better way to solve for X? (without using a graphing calc... )

Thanks alot and sorry for the messy equations
Derg

Originally Posted by Dergyll

Hey guys

Few days ago my teacher taught us about solving equations with degrees higher than 2, like x^3+2X^2+5X+12 or higher with x to the 4th of 5th. I can't help but get annoyed with synthetic division and long division, anybody know a better way to solve for X? (without using a graphing calc... )

Thanks alot and sorry for the messy equations
Derg

If you are asking for a formula for cubic equations, yes, it was discovered over 500 years. Ago, but schools do not teach it because it is extremely long (seriosly you never seen anything like that). Therefore, the only people that know of it, are people use are interested, like Quick,topsquark and myself.
Now the homework problems are MADE to be easily solved.

Thanks, so there is no other way of doing this...

Derg

Originally Posted by Dergyll

Thanks, so there is no other way of doing this...

Derg

There is something called "Cardano's Method" which you can always use to generate solutions to cubics. Warning: it's annoying to use! But you can look it up and see for yourself.

I don't know of the name of the system, but I have a posted method to solve quartic equations here. I don't know if it has a name or not. (It looks a bit messy without LaTeX.) It also is a bit hairy in actual use.

Both of these methods will solve general cubics and quartics. However as you can see things are not quite as simple as using the quadratic formula. I recommend division of polynomials to find solutions before trying either of these. The division can be much faster.

-Dan