import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from numpy.polynomial import Polynomial

f = Polynomial([2.0, 1.0, -6.0, -2.0, 2.5, 1.0])
a = -0.5
b = 1.3
m = (a+b)/2
e = 1e-6

list_a = []
list_b = []
list_m = []
list_f = []

root = 0.0

#+----------------------+
#| Start of your code   +
#+----------------------+
while True:
  list_a.append(a)
  list_b.append(b)
  list_m.append(m)
  list_f.append(f(m))
  if f(a)*f(m)<0:
    b=m
    m=(a+b)/2
    list_m.append(m)
    list_a.append(a)
    list_b.append(b)
    list_f.append(f(b))

  else:
    a=m
    m=(a+b)/2
    list_m.append(m)
    list_a.append(a)
    list_b.append(b)
    list_f.append(f(a))

  if (abs(list_m[-1]-list_m[-2])/abs(list_m[-1]))<=e:
    root=m
    break

#+--------------------+
#| End of your code   +
#+--------------------+

xs = np.linspace(-2.5, 1.6, 100)
ys = f(xs)

plt.axhline(y=0, color='k')
plt.plot(xs, ys)
plt.plot(root, f(root), 'ro')

print(pd.DataFrame({'a':list_a, 'b':list_b, 'm':list_m, 'f(x)':list_f}))