Question

Using Xo = 0 find an approximation to one of the zeros of x^3 − 4x +1 = 0 by using Birge Vieta Method. Perform two iterations

Answer 1

x_(n+1)=x_n-(x_n^3-4x_n+1)/(3x_n^2-4)
x_0=0;
x_1=0-1/(-4)=0.25;
x_2=0.25-(0.25^3-4*0.25+1)/(3*0.25^2-4)=0.25+0.0041=0.2541.