f(x) = x³ − 2x − 1

a. Show that the equation f(x) = 0 has a root, α, in the interval 1 < α < 2.

b. Using x₀ = 1.5 as a first approximation to α, apply the Newton–Raphson procedure once to f(x) to find a second approximation to α, giving your answer to 3 decimal places.