4. Let f(x) =-3x4- x2+ 2x+11. (a) Show that the equation f(x) = 0 has a unique root a in [-2, -1]. (b) Find the Newton's iterative formula for solving the equation f(x) = 0. [Give the formula in the form X, = g(X -1 ) where g(X,1) and h(X,,) are polynomial functions.] h(Xn-1 ) (c) Show that the sequence obtained by the iterative formula in (b) will converge to a for any initial guess x, in [-2, -1]. (d) Hence, with x, = -1.5, estimate the value of a correct to 4 decimal places. (25 marks) End of Paper Type here to search L 9:32 am C 26 C A D' E D ( () ENG 5/5/2022