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Thread: True/False Question

  1. #1
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    True/False Question

    If p(x) is a quadratic polynomial, then 1/p(x) can be put in the form A/(x-a) + B/(x-b) where a,b,A, and B are (real) constants.

    Could someone show me why this is true? I put false but got it wrong.

    Thanks,
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    The fundamental theorem of algebra! (Google it!)
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    ...

    not with all quadratic polynomial you can do what you describe.

    let,  p(x)=x^2+x+1, p(x) have no real roots.
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  4. #4
    A Plied Mathematician
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    ... and you would need to find real, unrepeated roots in order to do the partial fraction expansion (which is what this is) and end up with real numbers in all the places described.
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