Question

5. Find the seventh root of 125 using Bisection method, correct to three decimal places.​

Answer 1

Answer:

The situation to which we will apply the Intermediate Zero Theorem is:

Problem: We are given a function f(x) and an interval [a,b]. We know that f(x) changes sign on [a,b], meaning that f(a) and f(b) have opposite signs. We are also given a tolerance  > 0 (for "error"). Our task is to find a point c in [a,b] such that c is within  units of a root of f(x). In other words, so that there is a point z in [a,b] with f(z) = 0 and with |z - c| < .

If  = .00001, for example, we are asking to find a root of f(x) to within 5 decimal places.

Explanation:

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