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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 Ne
Posted: Thu May 12, 2022 10:27 am
by answerhappygod
- 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 Ne 1 (196.42 KiB) Viewed 21 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. [Give the formula in the form x, = g(x,-1) h(x,-1) where g(x,-1) and h(x,-1) are polynomial functions.] n n (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. =