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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.02i, 2i, 3i, and 3i?

KingGeorge
 3 years 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.

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

KingGeorge
 3 years 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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