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Basically, I understand that the solutions to quadratic equations (and if I remember correctly cubic equations) often had surveying problems land surveying. However, quartic and quintic equations seem to have less to do with the physical realities of societies in which their solutions were discovered that linear, quadratic, and cubic equations, especially since the problems were most often stated geometrically. The final proof of the unsolvability of polynomials of degree greater than 4 by radicals, though, came in the 19th century when mathematicians were studying the zeros of polynomials primarily for the sake of testing the solvability of polynomials in general.

So, I guess my question could be more accurately stated as: Were there any practical applications of finding the zeros of quartic and quintic equations at the time that the problems were solved?