Why use methods as Newton, ridder or secant method for root finding? Why use methods as Newton, ridder or secant method for root finding? I am bit confused for what reason someone would use these method to determine the root of a function, as it can easily be determined by solving $f(x) = 0$?

Not every equation can be solved without numerical methods. A few examples of some equations that "look easy" to solve, but can't be solved without numerical methods (at least, not in the way that you're thinking).

* $x^5 - x + 1 = 0$
* $\cos x = x$
* $\tan x = x$
* $e^x = 2x + 2$



Also, we need numerical methods to give us the decimal expansion to the "algebraic" answer, provided such an answer exists.