Question 762754
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The only way to solve this (or any other polynomial equation of degree 5 or greater) is by numerical approximation.  I graphed it and saw that there is a root very near -2, possible multiple roots at -1, and a root at 1.


A little polynomial long division gets you to the following result:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x\ +\ 1)^3(x\ -\ 1)(x\ +\ 2)(x^4\ -\ 2x^3\ +\ 5x\ -\ 4x\ +\ 4)\ =\ 0]


Plugging the coefficients of the quartic factor into an on-line <a href="http://www.akiti.ca/Quad4Deg.html">Quartic Solver</a>, I got the following results:


0.5   +   1.323 i
0.5   -   1.323 i
0.5   +   1.323 i
0.5   -   1.323 i


One pair of complex conjugates with a multiplicity of 2.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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