Provide an Appropriate Response $f ( x ) = x ^ { 2 } - ( 2 - i ) x - 2 i$

question 489

Multiple Choice

Provide an appropriate response.
-Is it possible to have a polynomial function whose only zeros are 2 and i? If so, write such a function. If not, explain why.

• A) No; the Complex Conjugate Zeros Statement requires that - i must also be a zero.
• B) Yes; \(f ( x ) = x ^ { 2 } - ( 2 - i ) x - 2 i\) is such a function.
• C) No; the Complex Conjugate Zeros Statement requires that \(- 2\) and \(- \mathrm { i }\) must also be zeros.
• D) Yes; \(f ( x ) = x ^ { 2 } - ( 2 + i ) x + 2 i\) is such a function.

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