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anonymous
 5 years ago
Find a polynomial function of least degree having only real coefficients with zeros as given.
3,2,i, and 2+i
anonymous
 5 years ago
Find a polynomial function of least degree having only real coefficients with zeros as given. 3,2,i, and 2+i

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0mrsheinold, if these are the zeros of your polynomial P(z) for z complex, then you have\[P(z)=(x+3)(z(2i))(z(2+i))\]All you need to do is expand this out to get your polynomial in a more amenable form:\[P(z)=z^3z^27z+15\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You'll always have real coefficients if your zeros are real or come in complex conjugate pairs, like you have...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok... I dont understand. The example in the book uses f(x) not P(z) im assuming thats ok.. but when I got my formulas at first I got f(x)=(x+3)(x2)(x+i)(x2i) how did you get your first formula??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f(x), P(z)...semantics, don't worry about it. Use what the book uses. You get the first formula by the following: if \[\alpha, \beta, \gamma\]are roots of a polynomial, f(x), then \[f(x)=(x{\alpha})(x\beta)(x\gamma)\]All you need to do is sub. your roots in.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0They are defined as roots of the equation because when x takes any of those values, one of the factors becomes zero, giving f(x)=0.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Not really. I have 4 numbers 3,2,i, 2+i I'm suppose to change the signs and put them in () So I thought 3 would change to (x+3) and the 2 would change to (x2) i would change to (x+i) and 2+i would change to (x2i) are those right or wrong??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh sorry bud, I read it as 2i, not 2,i...like I said, I'm ready for bed. Hang on...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0mrsheinold, since you are given 4 numbers two of which are complex, your desired polynomial should have 6 factors, P(x)=(x+3)(x2)(xi)(x+i)(x(2+i))(x(2i)) as stated above when you are given roots of a polynomial that are complex, those roots will appear in conjugate pairs. e.g. find the roots of P(x)=x^2+1
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