Question: Given the table below for the first 3 iterations, can you solve this table for 5 iterations (i.e., n=5 ) and conclude what the fifth approximation to the root (given by the column, 'c') will be? Bisection Algorithm An algorithm could be defined as follows. Suppose we need a root for f(x)=0 and we have an error tolerance of (the absolute error in calculating the root must be less that ). Bisection Algorithm: Step 1: Find two numbers a and b at which f has different signs. Step 2: Define c=2a+b. Step 3: If bc then accept c as the root and stop. Step 4: If f(a)f(c)0 then set c as the new b. Otherwise, set c as the new a. Return to step 1 . Example Exercise 1: Find a root of the equation x6x1=0 accurate to within =0.001. (Note: This equation has two real roots: -0.7780895987 and 1.134724138 \). First we have to find an interval where the function f(x)=x6x1 changes sign. Easy to see that f(1)f(2)