Finding Multiple Roots of Equations

In summary, the person is seeking help with finding the largest positive root of a function within a specific interval using different methods. They have written code for the bisection, Newton-Raphson, and secant methods, but are currently hard coding different intervals to find all of the roots. They have come across Horner's algorithm, which can find all roots if one is known, but are unsure of how to apply it to their problem. They are looking for a logical explanation, not code, on how to accomplish this task.
  • #1
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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  • #2
Hobbits over in the maths sub-forum might enjoy this.
 

Related to Finding Multiple Roots of Equations

1. What is the definition of "multiple roots" in equations?

In mathematics, multiple roots refer to the repeated solutions of an equation. This means that the equation has more than one value that satisfies it and makes it true.

2. How do you find multiple roots of equations?

There are several methods for finding multiple roots of equations, including the rational root theorem, factoring, graphing, and using numerical methods such as Newton's method. The best method to use depends on the complexity of the equation and the available tools.

3. Can equations have an infinite number of multiple roots?

No, equations can only have a finite number of roots, including multiple roots. This is because an equation represents a relationship between two quantities, and there can only be a finite number of distinct solutions to this relationship.

4. Are there any limitations to finding multiple roots of equations?

Yes, there can be limitations to finding multiple roots of equations. For example, some equations may not have any real solutions, or the solutions may be too complex to find using traditional methods. Also, some equations may have multiple roots, but they are not easily recognizable without advanced techniques such as calculus.

5. Why is it important to find all multiple roots of equations?

It is important to find all multiple roots of equations because they provide valuable information about the behavior of the equation and its solutions. They can also help in simplifying the equation and finding the most accurate and precise solution. In some cases, multiple roots can also reveal patterns and relationships between different equations.

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