How can clever school students understand the insolubility of the general quintic equation and higher degree polynomials in a few minutes? ?

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  • Dixon
    Lv 7
    2 months ago

    In a few minutes, I would explain and draw the variations of curve possible with a linear equation (not much), a quadratic (a bit more but not a lot - its basically scaling and offsets), then a cubic (quite a bit now). Then look at the general solution for a linear equation, a quadratic and a cubic (there is a general solution) - by which I literally mean just look at the formulas. It should then come as no surprise there is no general solution for higher order polynomials, just special cases.The complexity increases very rapidly with the order.

  • 2 months ago

    Unless you are a super genius, you do not understand anything within a few minutes.  You accept it as given until your experience and increasing knowledge makes you completely familiar with the basic elements of a topic, and all of its uses and consequences.  Nobody has a built-in understanding of advanced math.

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