Find a polynomial of degree $4$ , with integer coefficients that has zeros of $3 i$And $2$, with $2$
A double zero
A) $x ^ { 4 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 36 x - 36$
B) $x ^ { 4 } + 13 x ^ { 2 } - 4 x ^ { 3 } - 36 x + 36$
C) $x ^ { 4 } + 13 x ^ { 2 } + 4 x ^ { 3 } + 36 x + 36$
D) $4 x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 36 x - 36$
E) $x ^ { 4 } + 4 x ^ { 3 } + 5 x - 36$

Question

Quizplus · Accepted Answer

A polynomial with zeros of $3i$, $-3i$, and $2$ can be generated by the product 
$$(x-2)(x-3i)(x+3i)(x-2)$$
Simplifying this product yields the polynomial $x^4 - 4x^3 + 13x^2 - 36x + 36$. Thus, choice B is the correct answer.

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