The document discusses different methods for finding the roots or x-intercepts of equations, where the function f(x) equals 0. It focuses on closed methods like bisection, which works by repeatedly dividing an interval in half and determining if the root is in the upper or lower segment based on the sign change of f(x). As an example, it applies the bisection method to find the root of an equation within 7 iterations, obtaining a result with low error.

1. RUBEN DARIO ARISMENDI RUEDA

2. CHAPTER 4: ‘ROOTS OF EQUATIONS’

3. The roots of equations are the values of x that makes f(x)=0. There are many forms to obtain this values of x, but the most common is the quadratic formula. The other forms are mostly numerical methods and graphical methods that are used when is not to easy to find the root of the function.

4. There are some different kind of methods to find the roots of Equation: GRAPHICS OPEN METHODS CLOSE METHODS FIXED POINT NEWTON-RAPHSON SECANT FAKE POSITION BISECCION

5. http://s4.hubimg.com/u/351_f520.jpg f(x)=0

6. CLOSE METHODS. 1. Biseccion

7. The objective of this Method consist in divide the interval to the half, looking forward for the change of sings. If F(x) is Real and continous in the interval that goes from X(inf) to X(sup) and then there is at least 1 root between the intervals

9. THE ROOT WILL BE IN THE Inf. SEGMENT SO: Xi= STILL THE SAME Xs= THE LAST Xr THE ROOT WILL BE IN THE Sup. SEGMENT SO: Xi= THE LAST Xr Xs= STILL THE SAME

10. Example CALCULATE THE ROOT OF THE NEXT EQUATION. ERROR FOR THE NEW RESULT

11. In the table, we can see that the value in the 7th iteration is 0,42578125 which is approximate to the real value with an error of 0,00917431.