## caroo.salinaas19 Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 4; zeros: 2i and -3i one year ago one year ago

1. KingGeorge

In general, if you have a polynomial with real coefficients, and some complex root $$\alpha i$$ where $$\alpha$$ is a real number, the you also have the complex root $$-\alpha i$$. Using this, can you tell me what all the roots of your polynomial will be?

2. caroo.salinaas19

2i, -2i, -3i, and 3i?

3. KingGeorge

Bingo. So that means your factored polynomial will be $(x-2i)(x+2i)(x-3i)(x+3i).$Now you just have to expand it out.

4. caroo.salinaas19

i got this answer: x^3 -3ix^2-2ix^2+6ix^2-4xi^2+12i^2.

5. KingGeorge

Hmmm. I've definitely got something different. I'll walk you through the first few steps I did. $(x-2i)(x+2i)=x^2-2ix+2ix-(2i)^2=x^2-4(-1)=x^2+4$Note that $$i^2=-1$$ by definition. Similarly, $(x-3i)(x+3i)=x^2-3ix+3ix-(3i)^2=x^2-9(-1)=x^2+9$Using this, can you find $(x^2+4)(x^2+9)$on your own?