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(s^5)+(2*s^4)+(4*s^3)+(8*s^2)+10*s+6=0
Guest Aug 14, 2015

Best Answer 

 #1
avatar+26753 
+15

There is no general analytical solution for quintic algebraic equations, but a Newton-Raphson numerical method can be used:

 

 quintic solution:

So s ≈ -1.253462

 

There are four other solutions as well, but these are all complex.

.

Alan  Aug 14, 2015
 #1
avatar+26753 
+15
Best Answer

There is no general analytical solution for quintic algebraic equations, but a Newton-Raphson numerical method can be used:

 

 quintic solution:

So s ≈ -1.253462

 

There are four other solutions as well, but these are all complex.

.

Alan  Aug 14, 2015
 #2
avatar+87303 
+10

Here's the graph.......https://www.desmos.com/calculator/t1f4fhif21

 

[Desmos shows the root to be -1.25......Alan's answer is closer to the truth....!!!  ]

 

 

 

  

CPhill  Aug 14, 2015
 #3
avatar+26753 
+5

Thanks Chris.  I should have mentioned that it's always a good idea to draw a graph for these sort of problems, if only to get a good initial estimate to start off a more accurate numerical iteration method.

.

Alan  Aug 14, 2015

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