Using the given zero, find all other zeros of f(x). -2i is a zero of f(x) = x⁴ - 32x² - 144
2i, 12, -12; 2i, 6i, -6i; 2i, 6, -6; 2i, 12i, -12i

Solution:

Given f(x) = x⁴ - 32x² - 144 -2i is one of the zeros.

Zero of the functions means the solution which satisfies the given function.

Let x² =A ⇒ A² -32A-144

Use the quadratic formula

A ={ -b±√(b² -4ac)} / 2a

= {-(-32) ±√((-32)² -4(1)(-144)) / 2(1)

= {32 ±√(1024 +576)} /2

= (32 ± 40) /2

= 36, -4

A= x² = 36, -4

x= ±6, ±2i

Using the given zero, find all other zeros of f(x). -2i is a zero of f(x) = x⁴ - 32x² - 144
2i, 12, -12; 2i, 6i, -6i; 2i, 6, -6; 2i, 12i, -12i

Summary:

Using the given zero -2i, all other zeros of f(x) = x⁴ - 32x² - 144 are ±6, ±2i.