Question

X sin (πx - 2) + 1/2 = 0

Explain bisection algorithm

Answer 1

The bisection algorithm is a method used to find the roots of an equation by repeatedly dividing an interval and evaluating the function at the mid-point.

Step-by-step explanation:

The bisection algorithm is a method used to find the roots of an equation. It works by repeatedly dividing an interval into two equal sub-intervals and then determining in which sub-interval the root lies. This process is continued until the desired level of precision is achieved.

Here's how the bisection algorithm works:

1. Choose two initial values, a and b, such that f(a) and f(b) have opposite signs.
2. Calculate the midpoint, c, of the interval [a, b] using the formula: c = (a + b) / 2.
3. Evaluate the function at c: f(c).
4. If f(c) is close to zero (within a predefined tolerance), then c is the root.
5. Otherwise, determine whether the root lies in the sub-interval [a, c] or [c, b] based on the signs of f(a) and f(c) (or f(c) and f(b)).
6. Repeat steps 2-5 until the root is found.