Question

2. Find all 6 solutions (real and imaginary) to the equation. x6 = 64

using synthetic division please

using complex zeros

Answer 1

Let x6 = 64 = 64 (140) » XE = 64( cas ofisino) x= 2 ( casoti singo Using Demoiure's theorem =>x=, al cos (873) +isin ( 2 ) where k=0, 1, 2, 3, 4,5 Put x=0 * Xo = 2 ( caso tisino)= 2 Put X=1 *+1=2 / 6s 7 is in I) = 2/2 + 1) = Hirs Put x=2 =39 = 2 ( Cogan tisimng) = - Itinz

put x=3 >*3=2(-14 0i)=-2 put A=4 | 23(-5) - - - - - Ft x= r >x=0/- i) = 1-3 i X, X, , Tg, X3, Xy and as are 6 solutions ano