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Math Help - Anybody here good with theory?

  1. #1
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    Anybody here good with theory?

    Explain why :

    P(x) = x^50 - 5x^25 + x^2 - 1

    has no rational zeros. Use theory!
    Last edited by needhelp75; December 16th 2008 at 01:08 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by needhelp75 View Post
    Explain why :

    P(x) = x^50 - 5x^25 + x^2 - 1

    has no rational zeros. Use theory!
    The rational root theorem tell us that is this has a rational root it is of the form a/b where a is a divisor of the constant term and b a divisor of the coefficient of the highest power of the variable. So in this case all the rational roots (of any) are +1 or -1.

    Check if these are roots, if not this has no rational roots.

    CB
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  3. #3
    Eater of Worlds
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    Look into the Rational Root theorem. The possible candidates for real roots are 1 and -1 (why?)

    Does 1 or -1 satisfy the equation x^{50}-5x^{25}+x^{2}-1=0?.
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  4. #4
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    many thanks

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