Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the
polynomial in standard form.
-4 and $3 + 6 i$
A) $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 69 x + 180$
B) $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 69 x - 180$
C) $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 69 x - 179$
D) $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 69 x - 180$

Question

Quizplus · Accepted Answer

Given the zeros 4 and $3 + 6i$, we must also include the conjugate $3 - 6i$ to ensure real coefficients. The factors corresponding to these zeros are $x - 4$, $x - (3 + 6i)$, and $x - (3 - 6i)$. Multiplying these factors gives a polynomial $f(x) = (x - 4)(x - 3 - 6i)(x - 3 + 6i)$. When expanded, this yields $f(x) = x^3 - 10x^2 + 69x - 180$, matching option B.

Write a Polynomial Function of Minimum Degree with Real Coefficients 3+6i3 + 6 i3+6i

Write a Polynomial Function of Minimum Degree with Real Coefficients $3 + 6 i$