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Math Help - Finding nth degrees of polynomial functions

  1. #1
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    Finding nth degrees of polynomial functions

    find an nth degree polynomial function w/ real coefficients satisfying the given conditions:
    1. n = 4; -2,-1/2, and i are zeros; f(1)=18
    2. n = 4; -4, 1/3, and 2 +3i are zeros; f(1)=100


    I had a brain fart and don't remember how to do polynomial functions with fractions, I would like help to figure out what to do though.


    Thanks!
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  2. #2
    Junior Member MathTutor2013's Avatar
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    Re: Finding nth degrees of polynomial functions

    Hi,

    I post the answer for 1) :

    Since we have to find a 4th degree polynomial function w/ real coefficients
    and i itīs a zero then -i itīz a zero too

    Zeros are: -2,-1/2,i and -i

    f(x)=a(x+2)(x+1/2)(x-i)(x+i) = a(x+2)(x+1/2)(x^2+1)

    f(1)=a(3)(3/2)(2)=9a = 18

    Then a = 2

    Answer: 2(x+2)(x+1/2)(x^2+1)
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