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Finding a solution for an equation of the form *f*(*x*) = 0 is a frequently-encountered problem. It is not as easy to find roots of this equation as it might at first appear. Exact solutions are only possible if *f*(*x*) is a polynomial of degree *n* ≤ 9. By “exact solution,” we mean there is some procedure to calculate a root by using the parameters of the equation (as in the equation *ax*^{2} *+ bx + c = 0*). In what follows, the term “root of an equation *f*(*x*) = 0” will be used interchangeably with “zero of *f*(*x*)”.

The root finding procedure is based on an iterative process or, in other words, on a process of successive approximations. An iterative process has four stages:

1. Root localization – that is, finding an interval which ...

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