+0

# (s^5)+(2*s^4)+(4*s^3)+(8*s^2)+10*s+6=0

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

#1
+28029
+15

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

So s ≈ -1.253462

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

.

Aug 14, 2015

#1
+28029
+15

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

So s ≈ -1.253462

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

.

Alan Aug 14, 2015
#2
+101431
+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....!!!  ]

Aug 14, 2015
#3
+28029
+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.

.

Aug 14, 2015