newtonsmethod.sage

import numpy as np
x = var('x')
f(x) = (x-80)*(x-52.2)*(x-4.4)*(x+3)*(x+70.2)*(x+7.4)

fp = diff(f,x)

NewtonIteration(x) = x - f(x)/fp(x)

roots = []
for i in np.arange(-100.0, 100.0, 0.2):
    xn = i
    # avoid possible infinite cycle
    for j in range(100):
        xn_1 = N(NewtonIteration(xn),digits=20);
        if xn == xn_1:
            if xn not in roots:
                roots.append(xn)
            break
        xn = xn_1

print(roots)