find all the zeros of the polynomial

Question

Find all the zeros of the polynomial 

P(x)=x⁶-1

x1=, x2= with x1<x2

x3= ()+()i with both negative real and imaginary parts

x4= ()+()i with negative real part and positive imaginary part, 

x5= ()+()i with positive real part and negative imaginary part, 

x6= ()+()i with both positive real and imaginary parts. 

Answer 1

P(X) = X ^6 -1

 

       = (X^3 +1 ) ( X^3 - 1)

 

       = ( X +1 ) ( X^2 - X +1) ( X -1 ) ( X^2 + X + 1)

 

         X +1 = 0  X =-1     X -1 = 0  X =1

 

          X^2 -X +1 = 0    X = 1/2 ± √[(1^2 - 4( 1, 1)] /2

 

                                    X = 1/2 ± i √3

 

         X ^2 + X + 1 = 0     X = -1/2 ±i√3/2