Question

SHOW YOUR WORK!! Identify the simplest polynomial function having integer coefficients with the given zeros: 3i, −1, 2

Answer 1

Answer:

$p(x)=x^4-x^3+7x^2-9x-18$

Step-by-step explanation:

The given polynomial has roots 3i, −1, 2

Since $3i$ is a root $-3i$ is also a root.

The factored form of this polynomial is $P(x)=(x-3i)(x+3i)(x+1)(x-2)$

We need to expand to get:

$p(x)=(x^2-(3i)^2)(x^2-x-2)$

This becomes $p(x)=(x^2+9)(x^2-x-2)$

We expand further  to get:

$p(x)=x^4-x^3+7x^2-9x-18$