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: OPEN METHODS CLOSE METHODS GRAPHICS FIXED POINT NEWTON-RAPHSON SECANT FAKE POSITION BISECCION

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

6. CLOSE METHODS. 1. Biseccion

7. Theobjective of thisMethodconsist in divide theintervaltothehalf, looking forward forthechange of sings. If F(x) is Real and continous in theintervalthatgoesfrom X(inf) to X(sup) and thenthereis at least 1 root betweentheintervals

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

11. In thetable, we can seethatthevalue in the 7th iterationis0,42578125 whichisapproximatetothe real valuewithan error of 0,00917431.