A curve has equation $$$y=\mathrm{f}(x)$$$ where $$$\mathrm{f}(x)=x^{4}-5 x^{3}+6 x^{2}+5 x-15$$$. As shown in the diagram, the curve crosses the $$$x$$$-axis at the points $$$A$$$ and $$$B$$$ with coordinates $$$(a, 0)$$$ and $$$(b, 0)$$$ respectively. Use an iterative formula, based on the equation in part (b), to find the value of $$$a$$$ correct to 3 significant figures. Give the result of each iteration to 5 significant figures. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_22 Year：2020 Question No：7(c)

Answer:

Use iteration process correctly at least once
Obtain final answer $-1.24$
Show sufficient iterations to 5 sf to justify answer or show a sign change in the interval $[-1.245,-1.235]$

Knowledge points:

2.6.3 understand how a given simple iterative formula of the form relates to the equation being solved, and use a given iteration, or an iteration based on a given rearrangement of an equation, to determine a root to a prescribed degree of accuracy. (Knowledge of the condition for convergence is not included, but an understanding that an iteration may fail to converge is expected.)

Answer:

Knowledge points:

Solution:

Related Question