Question

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.

Answer 1

option B

which is roots are -2 and 2

Answer 2

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