Finding Multiple Roots of Equations

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SUMMARY

The discussion focuses on finding multiple roots of equations using various numerical methods, specifically the bisection method, Newton-Raphson method, and secant method. The user expresses difficulty in finding all roots without hard coding intervals and seeks guidance on utilizing Horner's algorithm for synthetic division to achieve this. It is established that knowing one root allows for the identification of all roots through polynomial division. The user requests a logical explanation rather than code examples.

PREREQUISITES
  • Understanding of the bisection method for root-finding
  • Familiarity with the Newton-Raphson method
  • Knowledge of the secant method
  • Basic principles of Horner's algorithm and synthetic division
NEXT STEPS
  • Research the implementation of Horner's algorithm for polynomial root-finding
  • Study the application of synthetic division in finding multiple roots
  • Explore advanced techniques for root-finding in numerical analysis
  • Learn about the limitations and advantages of each root-finding method discussed
USEFUL FOR

Students and professionals in mathematics, computer science, and engineering who are involved in numerical analysis and root-finding algorithms.

trouty323
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Homework Statement



Hello everyone. My task is to find the largest positive root in a specific interval of a function using the bisection method, Newton-Raphson method, and secant method. I've written code for all three of these methods, but the only way I can find all of the roots is to hard code different intervals. I know that is horrible practice, but the teacher never explained how to find them all using a different approach. However, I did read online that it can be done using Horner's algorithm (synthetic division). Basically, from my understanding, all of the roots can be found if one root is known. However, I could not find examples of code using Horner's algorithm specific to my purpose. I'm not asking for code, but a logical explanation as to how this can be accomplished. Thanks in advance!
 
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