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Math Help - Polynomial Proof

  1. #1
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    Polynomial Proof

    Prove that a polynomial P(x)X^4-3x^2+1 has exactly four radical.

    how can i do it?

    thanks.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    I'm not sure if that's the correct way to go about it, but my 2 cents:

    Using the quadratic formula, we get:

    x^2 = \dfrac{3 \pm \sqrt{9-4}}{2} =  \dfrac{3 \pm \sqrt{5}}{2}

    Then, taking the square root;

    x = \pm\sqrt{\dfrac{3 \pm \sqrt{5}}{2}}

    Since all the roots in there are real, (the square root of 5 is less that 3) there must be 4 real roots.
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  3. #3
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    so what is the 4 real roots>?
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  4. #4
    A Plied Mathematician
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    Unknown008 exhibited them in post # 2. Just take ++, +-, -+, -- combinations of the signs, and you'll get all four roots.
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