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Math Help - writing a function given zeros

  1. #1
    Newbie
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    writing a function given zeros

    i have to write a function gven the following zeros:

    -1, 2, 3+i, 3-i

    i know this: the highest exponent will be to the 4th
    the factors are: (x+1), ( x-2), and the other two i am not to sure...

    as you can see, i am stuck

    can anybody help
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  2. #2
    Senior Member JaneBennet's Avatar
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    3+\mathrm{i} and 3-\mathrm{i} are the roots of the equation x^2-6x+10=0. (Their sum is 6 and their product is 10.)

    Combine this with the linear factors.
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  3. #3
    Super Member wingless's Avatar
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    How about saying f = (x+1)(x-2)(x-3-i)(x-3+i) ?

    Then,

    f = (x+1)(x-2)(x-3-i)(x-3+i)

    f = (x+1)(x-2)\{[(x-3)-i][(x-3)+i]\}

    f = (x+1)(x-2)[(x-3)^2+1]

    ...
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