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  1. MHB Apprentice

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    #1
    Why we can't use radical to solve an equations with power greater than 4?

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  3. MHB Craftsman

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    #2
    You can solve certain equations with higher than 4:

    1. $x^n-a=0$
    2. $x^{2n}+x^n+a=0$
    3. $x^{3n}+x^{2n}+x^n+a=0$
    4. $x^{4n}+x^{3n}+x^{2n}+x^n+a=0$
    5. etc.

    where $a \in \Bbb{R}$ and $n\in \Bbb{N}$.

    However, the general fifth degree or higher polynomial does not have a radical solution due to a theorem, Abel-Ruffin Theorem. there is no solutions in radical to general polynomial equations of degree five or higher with arbitrary coefficients.

    Note: it does not assert some higher-degree polynomials have no solutions... (see at the beginning of the post)



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