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

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KingGeorge
 one year ago
Best ResponseYou've already chosen the best response.0In 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?

caroo.salinaas19
 one year ago
Best ResponseYou've already chosen the best response.02i, 2i, 3i, and 3i?

KingGeorge
 one year ago
Best ResponseYou've already chosen the best response.0Bingo. So that means your factored polynomial will be \[(x2i)(x+2i)(x3i)(x+3i).\]Now you just have to expand it out.

caroo.salinaas19
 one year ago
Best ResponseYou've already chosen the best response.0i got this answer: x^3 3ix^22ix^2+6ix^24xi^2+12i^2.

KingGeorge
 one year ago
Best ResponseYou've already chosen the best response.0Hmmm. I've definitely got something different. I'll walk you through the first few steps I did. \[(x2i)(x+2i)=x^22ix+2ix(2i)^2=x^24(1)=x^2+4\]Note that \(i^2=1\) by definition. Similarly, \[(x3i)(x+3i)=x^23ix+3ix(3i)^2=x^29(1)=x^2+9\]Using this, can you find \[(x^2+4)(x^2+9)\]on your own?
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