Question

Using the Newton Raphson method find the
Root x4-x-10=0​

Answer 1

Answer:

What is the root of the equation correct to decimal places using the Newton-Raphson method?

The equation has only two real roots.

Using the Newton-Raphson method, we can solve this equation as under:

Let

We want to determine the value of for which

Let the first estimate of be

Then, the second and better estimate would be

The third and better estimate would be

We continue in this manner until the difference between two successive estimates is lesser than the tolerable error.

For this particular case, taking the first estimate the details of the iterations are as under:

For the second root, taking the first estimate the details of the iterations are as under:

So, we get the solutions, correct to decimal places, as and