How to Find Roots of Equations Using Iteration Methods and Regula Falsi?

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SUMMARY

This discussion focuses on finding roots of equations using iteration methods, specifically the iteration method for the equation x3 - 3x + 1 = 0 and the Regula Falsi method for j(x) = ex - 3x. The first question emphasizes the need for a specific starting value and clarification on which root to find, as the cubic equation has three real roots. The second question seeks to apply the Regula Falsi method, requiring six iterations for an accuracy of four decimal places, highlighting the importance of understanding the function notation used.

PREREQUISITES
  • Understanding of numerical methods for root finding
  • Familiarity with the iteration method for solving equations
  • Knowledge of the Regula Falsi method (method of false position)
  • Basic calculus concepts, including functions and their roots
NEXT STEPS
  • Learn the specifics of the iteration method for root finding
  • Study the Regula Falsi method in detail, including its implementation
  • Explore the characteristics of cubic equations and their roots
  • Practice solving equations using numerical methods with different starting values
USEFUL FOR

Students, educators, and professionals in mathematics or engineering fields who are interested in numerical methods for solving equations and enhancing their problem-solving skills in calculus.

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This thread belongs to the homework section (do not repost though, the moderators will move it).

In order to get help, you need to show some efforts.
 
I've moved this to the homework section.

First question: Find the root of the equation [itex]x^3- 3x+ 1= 0[/itex] by iteration method (six decimal place accuracy).

There are a number of "iteration methods". Are you referring to a particular one? Why don't you select some starting value and show us how you would start the iteration? Also, this equation has 3 real roots. Which one do you mean by "the" root?

Second question: Use the method of Regula Falsi (method of false position) to solve the equation [itex]j(x)= e^x- 3x[/itex]. (Only six iterations are required, accuracy to 4 decimal places.)

First, was this exactly what the problem says? I don't see an equation, just a function- unless "j(x)" has some meaning you didn't mention.

What is "Regula Falsi"?
 
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