Form a polynomial f(x) with real coefficients having the given degree and zeros.
-Degree: 3; zeros: $- 3$ and $3 - 2 \mathrm { i }$
A) $f ( x ) = x ^ { 3 } - x ^ { 2 } + 11 x + 39$
B) $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 5 x - 52$
C) $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39$
D) $f ( x ) = x ^ { 3 } - x ^ { 2 } - 5 x + 39$

Question

Quizplus · Accepted Answer

Since the polynomial has real coefficients and a complex zero $3 - 2i$, its conjugate $3 + 2i$ must also be a zero. The polynomial is formed by $(x + 3)(x - (3 - 2i))(x - (3 + 2i))$, which simplifies to $x^3 - 3x^2 - 5x + 39$.

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Form a Polynomial F(x) with Real Coefficients Having the Given $- 3$