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Math Help - Finding Zeros in a Polynomial

  1. #1
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    Finding Zeros in a Polynomial

    Hey guys. I'm having trouble with this problem.

    Find all of the zeros of the following polynomial and give them in a comma-separated list. If there are no zeros, enter None .

    Note: complex numbers should be in the form (a+bi).
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  2. #2
    Senior Member topher0805's Avatar
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    First thing you should not is that when x=1, the function is equal to 0.

    Using long division, you can find that:

    x^4+4x^3-3x^2+8x-10 = (x-1)(x^3+5x^2+2x+10)

    Note that when x=-5 , (x^3+5x^2+2x+10)=0

    Using long division, you can find that:

    (x^3+5x^2+2x+10) = (x+5)(x^2+2)

    So we have that:

    x^4+4x^3-3x^2+8x-10 = (x-1)(x+5)(x^2+2)

    Now just find the values of x that make this expression equal to 0.
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  3. #3
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    ok, I see how the zeros are 1,-5,+2i and -2i. But how do I write 2i in a+bi form?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Haha

    Quote Originally Posted by badandy328 View Post
    ok, I see how the zeros are 1,-5,+2i and -2i. But how do I write 2i in a+bi form?
    2i in a+bi form is 0+2i
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