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Math Help - polynomial function with 3 zeros

  1. #1
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    polynomial function with 3 zeros

    i have a problem that states to find and simplify the polynomial function that has zeros of -3, 0, and 2i.

    my current work:

    f(x)=x(x+3)(x-2i)
    f(x)=(x^2 + 3x)(x-2i)
    f(x)=x^3 - 2ix^2 +3x^2 - 6xi

    Just wanting to see if I am doing this problem in the correct way.
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  2. #2
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    Quote Originally Posted by Cade02 View Post
    i have a problem that states to find and simplify the polynomial function that has zeros of -3, 0, and 2i.

    my current work:

    f(x)=x(x+3)(x-2i)
    f(x)=(x^2 + 3x)(x-2i)
    f(x)=x^3 - 2ix^2 +3x^2 - 6xi

    Just wanting to see if I am doing this problem in the correct way.
    = x^3 + (3 - 2i) x^2 - 6i x.
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  3. #3
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    Does your problem forbid your function from having additional zeros? If it does no then you could try the function:

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

    So

    f(x)=(x^3 - 2ix^2 +3x^2 - 6xi)(x+2i)
    f(x)=(x^4 - 2ix^3 +3x^3 - 6ix^2+2ix^3 + 4x^2 +6ix^2 + 12x)
    f(x)=(x^4 +3x^3+ 4x^2 + 12x)

    The advantage of this expression being that the coefficients are all real and it has all of the required zeros.
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