Explain-the false position method

Question

Response to the following :

Start with [a_o. b_o] and use the false position method to compute C_o, C₁ , c₂, and C₃.

1.    e^x — 2 — x = 0. [a_o. b_o] = [-2.4, —1.6]

2.    cos(x) + 1 — x = 0, [a_o. b_o]    = [0.8, 1.6]

3.    In(x) — 5 + x = 0, [a_o. b_o] = [3.2, 4.0]

4.    x² — 10X + 23 = 0, [a_o. b_o] = [6.0, 6.8]

(The problem is from Solution of Nonlinear Equations f(x) = 0 in Bracketing Methods for Locating a Root.)