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Math Help - Need help with constructing a polynomial

  1. #1
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    Need help with constructing a polynomial

    The problem is as follows:


    Construct a polynomial function, reducing all fractions to lowest terms.

    Third-degree, with zeros of 1-i, 1+i, and 4, and a leading cofficient of -5.

    Any ideas? My book has absolutely no help on this particular type of problem, and I cannot figure it out - I don't even know how to begin...

    Thank you in advance for any help...
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  2. #2
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    Quote Originally Posted by shipwreck View Post
    The problem is as follows:





    Any ideas? My book has absolutely no help on this particular type of problem, and I cannot figure it out - I don't even know how to begin...

    Thank you in advance for any help...
    p(x) = -5(x - 4) (x - [1 - i]) (x - [1 + i]) = -5(x - 4)([x - 1] + i)([x - 1] - i)

     = -5(x - 4)([x-1]^2 + 1) = -5(x - 4)(x^2 - 2x + 2) = \, ....
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