Question

5.5 (a) Determine the roots of f (x) = −12 − 21x − 2.75x3 graphically. In addition, determine the first
root of the function with (b) bisection and (c) false position.
For (b) and (c) use initial guesses of xl = −1 and xu = 0
and a stopping criterion of 1%.
5.6 Lo

Answer 1

Graphically:

Bisection method:

n	a	b	c	f(a)	f(b)	f(c )	diff (c)<10^(-5)
0	-1.00000	0.00000	-0.50000	11.7500	-12.000	-1.1563
1	-1.00000	-0.50000	-0.75000	11.7500	-1.1563	4.9102	FALSE
2	-0.75000	-0.50000	-0.62500	4.9102	-1.1563	1.7964	FALSE
3	-0.62500	-0.50000	-0.56250	1.7964	-1.1563	0.3019	FALSE
4	-0.56250	-0.50000	-0.53125	0.3019	-1.1563	-0.4314	FALSE
5	-0.56250	-0.53125	-0.54688	0.3019	-0.4314	-0.0658	FALSE
6	-0.56250	-0.54688	-0.55469	0.3019	-0.0658	0.1178	TRUE

Where we get the root

False position method:

n	a	b	c	f(a)	f(b)	f(c )	rel error	Less than 1%?
0	-1.00000	0.00000	-0.50526	11.75000	-12.00000	-1.03475
1	-1.00000	-0.50526	-0.54531	11.75000	-1.03475	-0.10267	0.07925	FALSE
2	-1.00000	-0.54531	-0.54924	11.75000	-0.10267	-0.01023	0.00722	TRUE

Where we get the root

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