Given two points on a graph (you know, each with a x-coordinate and a y-coordinate) which method could I use to determine the slope of a line between those two points? Which method could I use to determine the distance between those two points? Given three integer coefficients, A, B, C, which method could I use to solve a quadratic function of the form: Ax^2 + Bx + C = 0 ? Given four integer coefficients, A, B, C, D which method could I use to find the derivative of a cube polynomial function: Ax^3 + Bx^2 + Cx + D?
There's a proof in number theory that there's no formula for the zeroes of an order-5 polynomial (ie, p(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f), or any polynomial of greater order. OK, when I say "formula", I mean a function f(a, b, c, d, e, f) which yields the zeroes to p(x) above. IIRC there are formulae for the zeroes of polynomials of orders 3 and 4, but they're sufficiently complex that in almost all circumstances an approximation is better.