Bisection Method

"); grf.document.close(); } function expcls(){ grf.window.close(); } function tip(){ popup=window.open('','','toolbar=no,width=350,height=100,location=top'); popup.document.open(); popup.document.writeln("the intermediate value theorem for continuous functions "); popup.document.writeln("For any continuous function f (x) in the interval [a,b] which satisfies f (a) * f (b) < 0 must have a zero of 'f ' in the interval [a,b] ."); popup.document.writeln(""); popup.document.close(); } function tipclose(){ popup.window.close(); } function hlts(){ hlt=window.open('','','toolbar=no,width=350,height=250,location=top'); hlt.document.open(); hlt.document.writeln("highlights"); hlt.document.writeln("Advantages

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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4. Find the root of exp(-x) * (x²+5x+2) + 1= 0

exp4.jpg for exp[-x]*(x^2+5x+2)+1

The graph of this equation is given in the figure.

Let a = 0 and b = -1

Iteration No.	a	b	c	f(a) * f(c)
1	0	-1	-0.5	1.763 (+ve)
2	-0.5	-1	-0.75	-0.89 (-ve)
3	-0.5	-0.75	-0.625	-0.219 (-ve)
4	-0.5	-0.625	-0.562	0.076 (+ve)
5	-0.562	-0.625	-0.593	-0.015 (-ve)
6	-0.562	-0.593	-0.577	1.733*10^-3(+ve)

So one of the roots of exp(-x) * (x²-5x+2) + 1= 0 is approximately -0.577.