Bisection Method

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Iteration scheme is simple to implement.
Iterations always converge for any continuous function f(x).

Disadvantages

Convergence process is slow.
Always one has to find the interval [a,b] which brackets the zero of f(x)= 0 more importantly f(a) * f(b) must be less than zero.

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2. Find the root of x⁴-x-10 = 0

exp2.jpg for x^4-x-10

The graph of this equation is given in the figure.

Let a = 1.5 and b = 2

Iteration No.	a	b	c	f(a) * f(c)
1	1.5	2	1.75	15.264 (+ve)
2	1.75	2	1.875	-1.149 (-ve)
3	1.75	1.875	1.812	2.419 (+ve)
4	1.812	1.875	1.844	0.303 (-ve)
5	1.844	1.875	1.86	-0.027 (-ve)

So one of the roots of x⁴-x-10 = 0 is approximately 1.86.