Given the equation x^2 8x 10 cos(2x) + 15 = 0, find all the zeroes using fixed point iteration in Matlab, x_n+1 will be calculated using:

x_n+1 = 1/15 * x_n^2 + 7/15 * x_n - 2/3*cos(2x_n) + 1

The error shall be less than 10^-10

Plotting the function show four roots, around 2, 4, 5, and 6, which I used as start-guesses. I created a function where the current x was used to calculate the next according to the above formula. The error was calculated using:

error = abs(x-x_n)

Which might be wrong, as I could not find out how to calculate it. The results I got are:

x1 = 2.4297...

x2 = 5.715...

x3 = 5.715...

x4 = 5.715...

So x2 to x4 converged to the same value using the method, and I cannot see why. Any ideas?