
Newton's method
Newton's method assumes that the first derivative of the function is available. Suppose that the first and second derivatives are available as well. Design a second order Newton's method which uses f''[x], f[x], and f'[x] to predict the location of the root f. Compare this method to Newton's method and show that it converges faster.
So I have the formula for the second order Newton's method, which gives me an equation that requires using quadratic formula to solve. So I end up getting a + and  in the answer form, how am i supposed to predict the convergence if that is the case? Thank you!