Find an nth degree polynomial function with real coefficients satisfying the given conditions.
-$\mathrm { n } = 3 ; - 1$ and $3 + 2 \mathrm { i }$ are zeros; leading coefficient is 1
A) $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 7 x + 13$
B) $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 7 x + 13$
C) $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 15 x + 13$
D) $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x - 14$

Question

Quizplus · Accepted Answer

Given a 3rd degree polynomial with real coefficients, if $3 + 2i$ is a zero, its complex conjugate $3 - 2i$ must also be a zero. The zeros are $-1$, $3 + 2i$, and $3 - 2i$. The polynomial is $f(x) = (x + 1)(x - (3 + 2i))(x - (3 - 2i))$. Expanding this gives $f(x) = x^3 - 5x^2 + 7x + 13$.

Find an Nth Degree Polynomial Function with Real Coefficients Satisfying n=3;−1\mathrm { n } = 3 ; - 1n=3;−1

Find an Nth Degree Polynomial Function with Real Coefficients Satisfying $\mathrm { n } = 3 ; - 1$