Let, f(x) = x3-x-1 Now, f(1) = (1)3 - 1 - 1 = -1 < 0 f(1.5) = (1.5)3 - 1.5 - 1 = 0.88 > 0 Therefore, root lies between [ 1, 1.5 ] . Then, c = a - b - a f(b) - f(a) f(a) Then, c= 1-1.5 - 1 0.88 - (-1) (-1) Then, c= 1.27 a b f(a) < 0 f(b) > 0 c f(c) 1 1.5 - 1 0.88 1.27 - 0.24 < 0 1.27 1.5 - 0.24 0.88 1.32 - 0.02 < 0 1.32 1.5 - 0.02 0.88 1.32 --- Therefore, x = 1.32 is the required root.
