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Math Help - Polynom with real coeff

  1. #1
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    Polynom with real coeff

    Hi guys,
    I need to create a polynomial with real coefficients that has the roots 3,1, and -i. Then multiply and simplify.

    So far I have done this:

    (x-3)(x-1)=<br />
(x^{2}-4x+3)

    I know that -i= \sqrt{-1}
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  2. #2
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    Smile

    hi
    \left ( x-1 \right )\left ( x-3 \right )\left ( x^{2}+1 \right ) = {x}^{4}-4\,{x}^{3}+4\,{x}^{2}-4\,x+3,this polynomial has four roots -i,i,1,3.
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  3. #3
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    Quote Originally Posted by wykamikaam View Post
    Hi guys,
    I need to create a polynomial with real coefficients that has the roots 3,1, and -i. Then multiply and simplify.

    So far I have done this:

    (x-3)(x-1)=<br />
(x^{2}-4x+3)
    If -i is a root, then so is i (complex conjugates). So your polynomial would be
    (x - 3)(x - 1)(x - i)(x + i).

    Multiply it out to get your answer. (Note that (x - i)(x + i) = x^2 + 1.)


    01


    EDIT: Roah beat me to it...
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  4. #4
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    Thanks a lot to both of you!
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