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 February 1st, 2012, 06:05 AM #1 Newbie   Joined: Jan 2012 Posts: 1 Thanks: 0 polynomials Hi, My problem P=A +B*K +C*K^2 +D*K^3 +E*K^4 +F*K^5 how to express K in terms of the other variables or simply K= ???? please help me out
 February 1st, 2012, 06:56 AM #2 Senior Member     Joined: Feb 2010 Posts: 714 Thanks: 151 Re: polynomials In general this is not possible. Look up Abel, Galois, or quintic equation. For certain specific values you might be able to get a formula, but in general it cannot be done.
February 1st, 2012, 08:40 AM   #3
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Re: polynomials

Quote:
 Originally Posted by kunju P=A +B*K +C*K^2 +D*K^3 +E*K^4 +F*K^5
Usually shown this way:
A*K^5 + B*K^4 + C*K^3 + D*K^2 + E*K + F = 0

If you're lucky, all variables except F will equal 1, and F will equal -5

February 1st, 2012, 10:01 AM   #4
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Re: polynomials

Quote:
 Originally Posted by mrtwhs In general this is not possible. Look up Abel, Galois, or quintic equation. For certain specific values you might be able to get a formula, but in general it cannot be done.
kunju, what makes you think that there is a formula for solutions to a fifth degree polynomial?
If you have ax^2 + bx + c = 0, then you can solve for x..
Likewise, if you have ax^3 + bx^2 + cx + d = 0...
But not for a fifth degree polynomial..

 February 1st, 2012, 10:30 AM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Re: polynomials Or any higher degree (than four) for that matter.
 February 1st, 2012, 01:38 PM #6 Senior Member   Joined: Jul 2011 Posts: 245 Thanks: 0 Re: polynomials Well. . . We do have a solution to the quintic equation. However, we say that there is no solution in the sense that there is not a solution involving only the elementary operations of addition, subtraction, multiplication, division, exponentiation, and root extraction. There does not exist a solution to the quintic with solely these operations. However, there are far more behemous operations involving advanced analytical functions. We can express the solution in terms of these functions. This is a lot like how, when learning a new language, you can conceive of something complex to express. However, you can't really express it until you learn the more advanced aspects of the language.

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