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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
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

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KingGeorgeBest ResponseYou've already chosen the best response.0
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?
 one year ago

caroo.salinaas19Best ResponseYou've already chosen the best response.0
2i, 2i, 3i, and 3i?
 one year ago

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

caroo.salinaas19Best ResponseYou've already chosen the best response.0
i got this answer: x^3 3ix^22ix^2+6ix^24xi^2+12i^2.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.0
Hmmm. 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?
 one year ago
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