How can you find approximations to the zeros of a function?
Use Newton's method to recursively define sequences whose limits are zeros...
Given an approximation
#a_(i+1) = a_i - f(a_i)/(f'(a_i))#
We can use this formula to recursively define a sequence:
#a_0, a_1, a_2,...#
Then the limit of the sequence is a zero of
By choosing different values for the initial term
This method is both easy to apply and generally quite effective with polynomial functions.
It also works with both real and complex zeros.