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Math Help - Zeros of a function

  1. #1
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    Zeros of a function

    3. Find all rational zeros of the function:

    f(x)=25x^4+25x^3-154x^2-4x+24

    got no ide how to do it.

    4. Given that (1-i) is a zero of the function:

    f(x)=4x^4-11x^3+14x^2-6x

    Find all the zeros of the function.

    Now for question 4 i got [x-(1-i)], [x-(1-i)] as conjugates now i factor them which gives x^2-2x+2, and now when i use long division ikeep getting -12x^2 as a remainder??????
    Last edited by iFuuZe; April 20th 2012 at 12:20 AM.
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  2. #2
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    Re: Zeros of a function

    To get started you could evaluate f(x) with x= some factor of 24.

    Once you have one or two roots you could then use polynomial division.
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  3. #3
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    Re: Zeros of a function

    i dont understand what you mean mate
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  4. #4
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    Re: Zeros of a function

    Need to 'guess one solution' so we will have our 1st factor and can divide to find other factors. If ax-b is 1st factor a must be factor of 5 and b factor of 24.
    Last edited by biffboy; April 20th 2012 at 02:08 AM.
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  5. #5
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    Re: Zeros of a function

    For your second question, you're right to be dividing by x^2-2x+2. It's your division that's going wrong. You should get 4x^2-3x and no remainder.
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  6. #6
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    Re: Zeros of a function

    yep youre right now im not sure how i would go about factorising 4x^2-3x
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