The bisection method for finding roots involves starting with 2 values of a func

Question

The bisection method for finding roots involves starting with 2 values of a function, f(x), that have opposite sign. Since the function is continuous, there must be at least 1 root on the interval. This root can be found by sequentially calculating the function at the midpoint of the interval until a sufficiently precise root value is obtained. Please 1) write an algorithm for this method and 2) create a computation program to input any continuous function, f(x), and 3) for the function below, use your program to find the 3 roots to a precision/error level of 0.0001. Note the number of steps/computations needed to obtain solutions. f(x) = -2 - 0.01x + 1.5 x^2 - 0.2x^3

Explanation / Answer

Given a function f (x) continuous on an interval [a,b] and f (a) * f (b) < 0
Do
       c = (a+b)/2
       if f (a) * f (c) < 0 then b = c
                             else a = c
while (none of the convergence criteria C1, C2 or C3 is satisfied)

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