Question

using the method of false position :
(i) x3 - 4x + 1 = 0​

Answer 1

The method of false position, also known as the regula falsi method, is a root-finding algorithm that uses the concept of bisection to approximate the root of a function.

Here is one way to use the method of false position to solve for the root of the equation $x^3 - 4x + 1 = 0:$

First, you'll need to choose two initial guesses for the root, xl and xu. You can choose any two values that bracket the root, meaning that the function has opposite signs at the two values. For example, you could choose xl = 0 and xu = 1, since the function is positive at xl and negative at xu.

Next, you'll use the equation of false position to calculate a new approximation for the root, called xr. The equation is:

$xr = xu - (f(xu) * (xl - xu)) / (f(xl) - f(xu))$

Now you'll check the function value at xr and decide whether xr is a better approximation of the root than xl or xu. If f(xr) is close enough to zero, you've found the root. Otherwise, you'll need to repeat the process with a new set of xl and xu.

If the function at xr is of the same sign as the function at xl, it means that xr is to the left of the root and you will update xl = xr and repeat the process again. If the function at xr is of the same sign as the function at xu, it means that xr is to the right of the root and you will update

xu = xr and repeat the process again.

Repeat the process until the desired level of accuracy is reached.

Know more from the following links.

brainly.in/question/16766451

brainly.in/question/4211888

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