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: 706 Thanks: 141  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  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: polynomials Quote:
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  
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: polynomials Quote:
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: 7,950 Thanks: 1141 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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