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.
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