Bisection Method to Find Root of the Equation f(x) = x² - 3.

This MATLAB program finds the root of f(x) = x² - 3 using the Bisection Method. It keeps dividing interval & checks the error at each step.

The Bisection Method is a numerical technique used to find the root of a function within a given interval where the function changes sign. This method ensures convergence by iteratively halving the interval and selecting the subinterval that contains the root.

✅ User inputs initial bracketing values (a, b).

✅ Checks if f(a) and f(b) have opposite signs (valid interval).

✅ User inputs the number of iterations for refinement.

✅ Displays iteration-wise updates, including:

• Interval endpoints a and b.
• Function values f(a) and f(b).
• Midpoint c and its function value f(c).
• Error at each step.

✅ Outputs the final approximate root after the given iterations.

How to Use:

1️⃣ Run the script in MATLAB.

2️⃣ Enter the first bracketing value (a) and second bracketing value (b).

3️⃣ Ensure that f(a) and f(b) have opposite signs.

4️⃣ Enter the number of iterations for the method to refine the root.

5️⃣ The script will display each iteration’s results and the final approximate root.