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    Calculating the splitting field greatest common divisor

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    Assume F has characteristic 0 and K is a splitting field of f (x) in F[x]. If d(x) is the greatest common divisor of f(x) and f ' (x) and h(x) = f(x) / d(x) in F[x], prove that
    a) f (x) and h(x) have the same roots in K
    b) h (x) is separable

    © BrainMass Inc. brainmass.com December 24, 2021, 9:36 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/calculating-splitting-field-greatest-common-divisor-395721

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    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:36 pm ad1c9bdddf>
    https://brainmass.com/math/derivatives/calculating-splitting-field-greatest-common-divisor-395721

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