The modified Newton-Raphson method for finding the root of a function f(x) is given by:

x1 = x0 - f(x0)/f’(x0)

For a multiple root, we need to use the modified method, which involves dividing the function by its derivative squared:

x1 = x0 - f(x0)/[f’(x0)]^2 * [f(x0) * f’‘(x0)]/[f’(x0) * f’‘(x0)]

For f(x) = x^3 - 2x^2 - 4x + 8, we have:

f’(x) = 3x^2 - 4x - 4 f’‘(x) = 6x - 4

Substituting x0 = 1.2, we get:

f(1.2) = 1.728 f’(1.2) = -1.04 f’‘(1.2) = 1.2

Plugging these values into the modified formula, we get:

x1 = 1.2 - (1.728/(-1.04)^2) * (1.728 * 1.2)/(f’(1.2) * f’‘(1.2)) x1 = 1.99805

Therefore, the answer is (b) x1 = 1.99805.