f(x) = x⁴ − 3x³ − 6

a. Show that the equation f(x) = 0 can be written as  x =  ³√px⁴ + q, where p and q are constants to be found.

b. Let x₀ = 0. Use the iterative formula 

together with your values of p and q from part a, to find, to 3 decimal places, the values of x₁, x₂ and x₃.

The root of f(x) = 0 is α.

c. By choosing a suitable interval, prove that α = −1.132 to 3 decimal places.

Xn+1 = px + q.