# Finding Real roots of the Algebraic and Transcendental equations. Bisection Method

**Tutor description**

Analytically, we can usually choose any point in an interval where a change of sign takes place. However, this is subject to certain conditions that vary from method to method. And f(a) and f(b) have opposite signs. In this case a and b are said to bracket a root. the f must have at least one root in the interval (a, b). At each step the method divides the interval in two by computing the midpoint X1 = (a+b) / 2 of the interval and the value of the function f(X1) at that point. Unless X1 is itself a root (which is very unlikely, but possible) there are now two possibilities: either f(a) and f(X1) have opposite signs and bracket a root, or f(X1) and f(b) have opposite signs and bracket a root. The method selects the subinterval that is a bracket as a new interval to be used in the next step.

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