Newton-Raphson Formula question

  • Thread starter Thread starter synkk
  • Start date Start date
  • Tags Tags
    Formula
Click For Summary
SUMMARY

The discussion focuses on finding the smallest positive root of the equation x4 + x2 - 80 = 0 using the Newton-Raphson method. A starting point of x = 3 is suggested, as it is close to the expected root. Participants confirm that while the equation can be solved analytically, the Newton-Raphson method is still applicable for numerical approximation. The conversation emphasizes the importance of selecting an appropriate initial guess for effective convergence.

PREREQUISITES
  • Understanding of the Newton-Raphson method for root finding
  • Familiarity with polynomial equations and their properties
  • Basic knowledge of numerical methods in calculus
  • Ability to perform iterative calculations
NEXT STEPS
  • Study the derivation and application of the Newton-Raphson method
  • Explore analytical solutions for polynomial equations
  • Learn about convergence criteria for iterative methods
  • Investigate alternative numerical methods for root finding, such as the Bisection method
USEFUL FOR

Mathematicians, engineering students, and anyone interested in numerical analysis or solving polynomial equations using iterative methods.

synkk
Messages
216
Reaction score
0
Question:
Find the smallest positive root of the equation x^4 + x^2 - 80= 0 correct to two decimal places. Use the Newton-Raphson process.

How would I go about finding the smallest positive root? What I was thinking is using x = 3 as x = 3 is the largest number that would be close to 0 (for the equation), then finding an approximation for that, is that correct?

thanks.
 
Physics news on Phys.org
1) Independent of the question asked, can you see that the equation is trivially solvable exactly analytically (no need for Newton-Raphson)?

2) For a numeric solution, a start value of 3 looks fine. I assume (hope) you know how to apply Newton-Raphson from there.
 
Last edited:
PAllen said:
1) Independent of the question asked, can you see that the equation is trivially solvable exactly analytically (no need for Newton-Raphson)?

2) For a numeric solution, a start value of 3 looks fine. I assume (hope) you know how to apply Newton-Raphson from there.

I'm perfectly aware it is solvable from that form, and I do know how to apply Newton-Raphson. Thanks.
 

Similar threads

Iterative root finding for the cube root of 17
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad Make Intelligent Initial Guesses for Newton-Raphson Programmatically
  • · Replies 16 ·
Replies
16
Views
5K
Graduate How to use the Newton-Raphson method while keeping the sum constant?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Newton-Raphson Method With Complex Numbers
  • · Replies 7 ·
Replies
7
Views
3K
What Is the Smallest Positive Argument for the Sum of Complex Roots of Unity?
  • · Replies 27 ·
Replies
27
Views
5K
Find the value of ##a, b## and ##k## in the problem involving graphs
  • · Replies 6 ·
Replies
6
Views
2K
Solving Homework Questions: Modulus, Arg, Roots
  • · Replies 3 ·
Replies
3
Views
2K
Find integer points on this equation
  • · Replies 8 ·
Replies
8
Views
2K
Number of ways of arranging 7 characters in 7 spaces
  • · Replies 8 ·
Replies
8
Views
2K
How Do You Solve Complex Number Equations in Quadratics and Exponentials?
  • · Replies 39 ·
2
Replies
39
Views
6K