- #1

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^{2}+ bx + c, why is it not possible to simply differentiate both sides, and produce 0 = 2ax + b, and solve for x, instead of going through the drudgery of the quadratic equation?

My knowledge of calculus tells me that it is because 0 = ax

^{2}+ bx + c is not a function, and is only fulfilled by 2 real values, but I want there to be deeper reason. =|