Samagra G.

asked • 06/27/16

complex roots

if Z1 , Z2 , Z3, Z4 are roots of equation z4 + z3 + z2 + z + 1 = 0
 
then what is the sum of all the fourth and fifth power of roots ?

3 Answers By Expert Tutors

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Degonimia H. answered • 07/01/16

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Sanhita M. answered • 06/27/16

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Mathematics and Geology

Samagra G.

but z=1 is not satisfying the equation
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06/27/16

Sanhita M.

I'll get back to you as soon as I can resolve.
 
 
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06/27/16

Sanhita M.

As I tested the given polynomial w.r.t imaginary roots of 1 , the last term of the given polynomial having possible real factors +1, -1, and possible imaginary factors +√-1,-√-1, by synthetic division the results are having remainders equal to -1. Therefore, none of the factors of 1 is actually a root of the polynomial, hence the equation does not hold for any of the factors of 1. Moreover, it seems that either the expression is incomplete or wrong. If not, then please provide the solution when you get one. 
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06/28/16

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