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Chapter 5. Finding Roots

“Solve for x” is typically what we're asked to do when given an equation involving x as the unknown. One way to do it is to rewrite the equation into the form f(x) = 0, and then find the roots, or the zeros, of the function. In other words, we want to find the values of x such that f(x) = 0. Depending on the function, there may be more than one root, and they can be either real or complex, or there may be no roots at all. If we draw a graph of f(x) in the xy plane, then the real roots are those values of x wherever the plot crosses the x axis. This chapter explores various algorithms for finding real roots that are suitable for a computer.

Traditionally, these algorithms are called methods, as in bisection method and Newton's ...

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