Bracketed roots.

(1) Define a function f(x) {return x*x-7}

(2) Find left and right brackets for a root, call them LL=2; UL=3

(3) Assign a value to the tolerance HH=0.0001

output: value R, such that there is a value of x in the open interval defined by R - HH/2 < x < R + HH/2 where f(x) = 0

Note that x may be irrational or something else that does not exist in our number space.

One of these values needs to be calculated using the binary search algorithm and the other one should use the false position algorithm. Be careful with false position to make sure that you start with an interval on which the algorithm terminates.

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