SOLVE: X(2X2 +1)=15

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section: Chapter Questions
Problem 9CT
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SOLVE:

X(2X2 +1)=15

Expert Solution
Step 1

Let the function is  F(x) = 2x3 + x -15.

 

F(x) is negative at x = 1 and positive at x = 2, so the root of the function lies between the interval (1,2).

 

Algebra homework question answer, step 1, image 1
Step 2

 

By using the Newton-Raphson method, we approach one root of a function by iterative process. Let start the process with arbitrary initial value x0 =1.5.

 

According to the Newton-Raphson Method

Algebra homework question answer, step 2, image 1
Step 3

For the next approximation, the other value is x1=1.9655 from the above calculation:

Algebra homework question answer, step 3, image 1

Algebra homework question answer, step 3, image 2
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