math6601_projects/homework10/comment.txt

For problems (a) and (b), which have real roots, all methods converged; Newton's method was the fastest (quadratic), followed by the Secant method (superlinear), with the Chord method being the slowest (linear). However, for problem (c) (x^2 + 1), which has no real roots, all methods failed: the Chord method rapidly diverged to infinity, while Secant and Newton's method oscillated.