Bisection Method Calculator: Interactive Root-Finding Tool

What is the Bisection Method?

The Bisection Method is a simple and robust numerical technique used to find the roots of a continuous function. It works by repeatedly bisecting an interval and then selecting the subinterval in which the root must lie for further processing.

Learn more about how it works

1. Start with an interval [a, b] where f(a) and f(b) have opposite signs.
2. Calculate the midpoint c = (a + b) / 2.
3. Evaluate f(c).
4. If f(c) = 0 (or is very close to 0), c is the root.
5. If f(c) has the same sign as f(a), update a = c. Otherwise, update b = c.
6. Repeat steps 2-5 until the desired accuracy is achieved or the maximum number of iterations is reached.

Input Parameters

Try these:

x³ - x - 10 (1, 3)

x² - 4 (0, 3)

sin(x) - 0.5 (0, 2)

log(x) (1, 3)

x² + x - 6 (1, 4)

Function f(x):

Interval Start (a):

Interval End (b):

Number of Iterations:

Steps & Output

How to Read the Table

This table shows the iterative steps of the Bisection Method:

• Iteration: The current step number.
• a: The left endpoint of the interval.
• b: The right endpoint of the interval.
• c: The midpoint of the interval (a+b)/2.
• f(a): The function value at (a).
• f(b): The function value at (b).
• f(c): The function value at (c), the midpoint.

Iteration	a	b	c (Midpoint)	f(a)	f(b)	f(c)

Function Graph

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