Verified answer

x^2 + 4 has two complex (imaginary) roots.

x^4 - 16 has four roots (two complex and two real).

The factors of x^4 - 16 are (x^2 + 4) and (x^2 - 4), or

(x^2 + 4), (x - 2), and (x + 2).

To find the roots:

x^2 + 4 = 0

x = +/- 2i

x - 2 = 0

x = 2

x + 2 = 0

x = -2

So, there are four roots:

2i, -2i, 2, -2

C. is correct for the original polynomial x^4 - 16.

f(x) = x^4-16 = (x²+4)*(x + 2)(x - 2)

f has roots of x = +/- 2

Choice C

X2+4= X6

x^4-16= x^-12

which equals x7^-12