Another method for finding a root of a polynomial P(x) is Newton's method. This method consists of taking an initial approximation Xl and constructing a tangent line to the graph of P(x) at that point.
The point x2 where this tangent line crosses the X axis is taken as the second approximation to the root.
Then another tangent line is constructed at x2, and the point x3 where this tangent line crosses the x axis is the next approximation.
The following diagram shows this process:
