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June 11th, 2019, 02:44 PM  #1  
Newbie Joined: Jun 2019 From: iran Posts: 4 Thanks: 0  can anyone help me with this understanding of quintic equations?
this is the context: Quote:
Quote:
 
June 11th, 2019, 02:48 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,386 Thanks: 746 
The general quintic is $a x^5 + b x^4 + c x^3 + d x^2 + e x + f$. There is no general algebraic formula that determines the value of $x$ for arbitrary $a, b, c, d, e$, and $f$. By algebraic formula I mean a formula involving addition, subtraction, multiplication, division, and root extraction. For example you may be familiar with the famous quadratic formula to solve a second degree equation. There are also formulas to solve third and fourth degree equations. But there is no general formula to solve equations of fifth degree or higher. Perhaps the wording you quoted is a little confusing. They don't mean you are solving for the coefficients. They mean there's no formula to find $x$ given arbitrary coefficients. Last edited by Maschke; June 11th, 2019 at 02:52 PM. 
June 11th, 2019, 02:50 PM  #3  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,270 Thanks: 934 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Is that what you are looking for? Dan  
June 11th, 2019, 03:03 PM  #4 
Newbie Joined: Jun 2019 From: iran Posts: 4 Thanks: 0 
When you guys explain it in this way I get it perfectly but when I read the sentence mentioned, I would be again confused. I don't get it why is written solutions for every single coefficient. if you want it to rewrite that sentence what would you say, because I think my confusion is coming from the style of writing of the writer.
Last edited by amirsoly; June 11th, 2019 at 03:13 PM. 

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