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Solution to the Pentic

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  • Jon
    The roots to the equation, ax^5+bx+c=0 are the roots to the quadradic, ((a^2)*(a^2+b^2))x^8 + (a*(b^2)*c)x^4 - ((a^2)*b*c+(b^2)*(a^2+b^2))=0 DEVELOPMENT
    Message 1 of 2 , Dec 2, 2009
      The roots to the equation,

      ax^5+bx+c=0

      are the roots to the quadradic,

      ((a^2)*(a^2+b^2))x^8 + (a*(b^2)*c)x^4 - ((a^2)*b*c+(b^2)*(a^2+b^2))=0

      DEVELOPMENT

      http://jons-math.bravehost.com/pentic.html

      One plane passes through the origin. The other parallel plane is displaced
      by the distance between the two planes. The projection of the curve on one
      plane is the same as on the other. However, the plane passing through the
      origin cancels x. The projection of the curve on this plane is mapped back
      up to the displaced plane and the solution precipitates.

      Jon Giffen (c) 2009
    • Jon
      Message 2 of 2 , Dec 2, 2009
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