y = f(x), where f(x) = x² sin x − 2x + 1. The points P, Q, and R are roots of the equation. The points A and B are stationary points, with x-coordinates a and b respectively.

a. Show that the curve has a root in each of the following intervals:

i. [0.6, 0.7]

ii. [1.2, 1.3]

iii. [2.4, 2.5]

b. Explain why x₀ = a is not suitable to use as a first approximation to α when applying the Newton Raphson method to f(x).

c. Using x₀ = 2.4 as a first approximation, apply the Newton–Raphson method to f(x) to obtain a second approximation. Give your answer to 3 decimal places.