Unexpected Output From Newton's Method

I have this code for solving Newton's method and in the last iteration, the output values have come wrong. Those values should not be negative as I checked it manually on paper. As

Solution 1:

Ah, I see now.

Just as you say,

float(poly_substitute(poly, x))

evaluates to -0.015. Then,

float(poly_substitute(poly_diff, x))

evaluates to -0.01. Thus, substituting for these values and for x,

x_n = 0.5 - ( (-0.015) / (-0.01) )
x_n = 0.5 - 0.6666666...
x_n = -0.166666...

Your manual math was what was at fault, not the code.

Solution 2:

The polynomial as given has a single solution at x = 0. The code is working fine.