4. Let f(x)=-5x4 - 2x² + 4x +14. (a) Show that the equation f(x) = 0 has a unique root a in (-2,-1]. (b) Find the Newton

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4 Let F X 5x4 2x 4x 14 A Show That The Equation F X 0 Has A Unique Root A In 2 1 B Find The Newton 1 (37.23 KiB) Viewed 34 times

4. Let f(x)=-5x4 - 2x² + 4x +14. (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. g(x,-1) [Give the formula in the form x. where g(x-1) and h(x,-1) are polynomial functions.] h(x-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, estimate the value of a correct to 4 decimal places. 0