Step 1 :

The function is \"\" in the interval \"\".

\"\"

It follows that \"\" . we can therefore apply intermediate value theorem to conclude that there must be some c in \"\" such that \"\"

Step 2:

Now we use bisection method for approximating the real zeros of a continuous function.

In this approximation if \"\" , then the zero must lie in the interval \"\"

a b (a+b)/2 f[(a+b)/2]
0 1 0.5 -0.375
0.5 1 0.75 0.171
0.5 0.75 0.625 -0.130
0.625 0.75 0.6875 0.01245
0.625 0.6825 0.653 -0.066
0.653 0.6825 0.668 -0.033
0.668 0.6825 0.67525 -0.01686
0.67525 0.6825 0.678 -0.01033
0.678 0.6825 0.68025 0.00497

The approximated value of zero is \"\" , \"\".

Step 3:

Now we have to find out zero value using  graphical approach.

\"\"

From the above graph the zero value is nearly 0.68 , it is located between 0.6 and 0.7.

Step 4:

To find out the accurate value of value we further need to zoom the graphing utility as shown below.

\"\"

We clearly observe from the above graph the zero value is nearly 0.6823. 

Solution:

The zero value approximated to two decimal points is 0.68.

The zero value approximated to four decimal points is 0.6823.