In numerical, the bisection method is a method used to find the root that can be applied to any continuous functions for which two values of opposite signs are known. It is the simplest iterative method which is also known as the half-interval method or bolzano method.

In this method first, a sufficiently small interval $\mathbf{[}{\mathbf{a}}_{\mathbf{0}}\mathbf{,}\mathbf{ }{\mathbf{b}}_{\mathbf{0}}\mathbf{]}$ is found out containing the root by the method of tabulation. 

Now, if 

PROCEDURE

We start the sequence of iteration by setting, 

Next, we have to set

and we have to repeat the above process till we obtain

with the desired accuracy. 

GRAPHICAL REPRESENTATION OF BISECTION METHOD:

INPUT:

OUTPUT:

PROCESS:

Step 1: [Defining a function to find the root]

function f(x)
$\mathrm{f}\left(\mathrm{x}\right) = {\mathrm{ax}}^2 + \mathrm{bx} + \mathrm{c}$
return the value of f(x)
[End of function f(x)]

Step 2: [Method to perform bisection method]

Step 2.1: Set a <- -1.0
Set b <- 0.0
Set x <- 0.0
Set y <- 0.0

Step 2.2: While(f(a) × f(b) > 0) repeat
Set a <- b
Set b <- b + 1.0
[end of ‘while’ loop]

Step 2.3: Take the error (the accuracy) from the user

  	Step 2.4: if f(a) > 0 then
     			Set a <- a + b
     			Set b <- a - b
      			Set a <- a - b
     		[End of ‘if’]
     		
  	Step 2.5: Set y <- x
       	  	 Set x <- (a + b)/2
        	 If f(x) < 0 then
          	 	Set a <- x
       	  	else
         	  	Set b <- x
[End of ‘if’]
          	Print a, b, x, f(x)
      While fabs(x - y) > err repeat Step 2.5
[End of bisection method]