Question

X⁴-x-10 by regula falsi method
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Answer 1

Answer:

What is the root of the equation x4−x−10=0 correct to 4 decimal places using the Newton-Raphson method?

x4−x−10=0⇒x4=x+10.

⇒x4≈10⇒x≈±10−−√4≈±1.75.

The equation has only two real roots.

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

Let f(x)=x4−x−10⇒f′(x)=4x3−1.

We want to determine the value of x for which f(x)=0.

Let the first estimate of x be x1.

Then, the second and better estimate would be x2=x1−f(x1)f′(x1).

The third and better estimate would be x3=x2−f(x2)f′(x2).

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 x1=−1.75, the details of the iterations are as under:

For the second root, taking the first estimate x1=1.75, the details of the iterations are as under:

So, we get the solutions, correct to 4 decimal places, as x=−1.6975 and x=1.8556.

Answer 2

Answer:

Step-by-step explanation: