The polynomial equation x^6-16x^2=4x^4-64 has complex roots + - 2i. What are the other roots? Use a graphing calculator and a system of equations.

Use u subsitution the solve by grouping

u=x^2

u^3-16u=4u^2-64

u^3-4u^2-16u+64=0

(u^3-4u^2) + (-16u+64) = 0

u^2 (u-4) + (-16) (u-4) = 0

(u^2-16) (u-4) = 0

(u-4) (u+4) (u-4) = 0

(u+4) (u-4) ^2=0

u=x^2

(x^2+4) (x^2-4) ^2=0

(x^2+4) ((x-2) (x+2)) ^2=0

(x^2+4) (x-2) ² (x+2) ²=0

set to zero

x^2+4=0

x^2=-4

x=+/-2i

x-2=0

x=2

x+2=0

x=-2

the other roots are - 2 and 2

for graphinc calculator, graph and find x intercepts