Form a polynomial f(x) with real coefficients having the given degree and zeros.
-Degree 3: zeros: $1 + i$ and $- 9$
A) $f ( x ) = x ^ { 3 } + x ^ { 2 } - 16 x + 18$
B) $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 18 x - 16$
C) $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18$
D) $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } - 16 x - 12$

Question

Quizplus · Accepted Answer

The polynomial must have real coefficients, so the complex conjugate of $1 + i$, which is $1 - i$, must also be a zero. The polynomial is formed by $(x - (1+i))(x - (1-i))(x + 9)$, which simplifies to $x^3 + 7x^2 - 16x + 18$.

Form a Polynomial F(x) with Real Coefficients Having the Given 1+i1 + i1+i

Form a Polynomial F(x) with Real Coefficients Having the Given $1 + i$