The first approximation to the root of x^2 - 2 = 0 in the interval [1, 2] by the regula falsi (false position) method is

Explanation

With f(1) = -1 and f(2) = 2, x1 = (1 x 2 - 2 x (-1)) / (2 - (-1)) = 4/3 (3/2 is the bisection point and 7/5 is the next regula falsi iterate).