Write a polynomial f (x) that meets the given conditions.
-Polynomial of lowest degree with real coefficients and zeros $4 i$ and $2 - i$.
A) $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 12 x ^ { 2 } + 64 x - 64$
B) $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 19 x ^ { 2 } - 64 x + 48$
C) $f ( x ) = x ^ { 4 } + 4 x ^ { 3 } - 12 x ^ { 2 } - 64 x + 64$
D) $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 21 x ^ { 2 } - 64 x + 80$

Question

Quizplus · Accepted Answer

The polynomial must include the conjugates of the given zeros, $ -4i $ and $ 2 + i $, resulting in a polynomial of degree 4. Option D satisfies this condition.

Write a Polynomial F (X) That Meets the Given Conditions 4i4 i4i

Write a Polynomial F (X) That Meets the Given Conditions $4 i$