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.

Question

Quizplus · Accepted Answer

The Complex Conjugate Root Theorem states that if a polynomial has real coefficients and a complex number $a + bi$ is a root, then its complex conjugate $a - bi$ must also be a root. Therefore, if $i$ is a root, $-i$ must also be a root.

Provide an Appropriate Response f(x)=x2−(2−i)x−2if ( x ) = x ^ { 2 } - ( 2 - i ) x - 2 if(x)=x2−(2−i)x−2i

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