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I'm helping my son with Math in high school. He is now learning to solve higher order equations, with for example $x^4$, $x^3$ or $x^5$. The point is that he sees no use in solving these equations (apart from an algebraic challenge) because for him they serve no purpose.

The quadratic equation is easy to illustrate by applying it to a ball you throw upward.

Would you have some examples of real-life systems where higher order equations are used?

Tks!

Larry
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kxtronic
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  • Following your example, any motion with non-constant acceleration requires a higher order polynomial to be described. – Javi Sep 29 '18 at 10:47
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    See https://math.stackexchange.com/a/2197191/589 – lhf Sep 29 '18 at 10:48
  • Maybe you could try approaching these problems from a numerical or statistical point of view. For example you have take samples or made many observations and now you try to find a curve approximating these. You could also try to explain him the ideas of the Taylor and Fourier Series as how "laying multiple polynomial (!) functions over another" help to approximate weird/complicate looking functions. Theoretically you could also try to explain what characteristic polynomials and a system of linear equations are connected, however this might be tricky for a high schooler. – Imago Sep 29 '18 at 11:00

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