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Root bracketing methods
Root polishing methods
Newton method is the standard rootpolishing algorithm.
Newton method, also called the NewtonRaphson method, is a rootfinding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a suspected root.
Newton algorithm begins with an initial
guess for the location of the root. On each iteration, a line
tangent to the function f is drawn at that position. The point
where this line crosses the xaxis becomes the new guess.
Newton method converges quadratically for single roots, and
linearly for multiple roots.

The function below, written in Pascal, takes a simpler aproach, ignoring the situation in which Newton method does not converge. For a C implementation of Newton method, grasp Newton.c.
To find more about Newton method, visit the pages below:
Numerical methods  Bisection method  Regula Falsi method  Brent method  Newton method  Secant method
See how Newton method works, solve equations free and take the results with you.