A. Non-Linear Equations—one at a time
There are closed form solutions for quadratic and even 3rd degree polynomial equations. Higher degree polynomials can sometimes be factored. However, in general there is no closed form analytical solution to non-linear equations.
a. Roots & zeroes
We seek to find x such that  or perhaps such that  . In the latter case, we merely set  . We are looking for a root of the equation or a zero of the function f(x).
b. Graphical solution
Plot f(x) vs. x—observe where the graph crosses the x-axis or plot f(x) and g(x) vs. x and observe where the two curves intersect. A graph won’t give a precise root, but we can use the graph to choose an initial estimate of the root.
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