The method for determination of a root of a non-linear equation which uses two initial guess roots but does not require that they must bracket the root, is?

The method for determination of a root of a non-linear equation which uses two initial guess roots but does not require that they must bracket the root, is? Correct Answer Secant method

Concept:

Methods to find the root of non-linear roots:

The methods to find the non-linear roots are:

1. Bisection method
2. Regular falsi method
3. Newton Rapson Method
4. Secant method etc

Calculation:

As mentioned above we can determine the roots of a non-linear equation by using any of the mentioned methods.

• The First method is the Bisection method. If a function f(x) = 0 has at least one root in the interval where f(a) and f(b) have different signs then we can use this method where we use f(a) and f(b) to bracket a root.
• The second method is regular falsi method. This method is also used to solve a problem of the type f(x) = 0 by using two false roots and further we bracket a root and use it to approximate the root.
• The next method is the Newton-Rapson method. The Newton Rapson method is used to find the root where the function is differentiable and of the type f(x) = 0. We use derivatives at a bracketed root to approximate the root.
• The last method is the secant method. The secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. Here we use successive difference approximation from Newton's method.

All the methods use two initial guess roots but only the secant method does not use the bracket to the root to determine the final outcome.

Thus the correct answer is the Secant method.