Question

Given: x³+x-4=0, x[1;4]

a) Find the minimum number of bisection method iterations needed to achieve an approximation of the root with 10^-3.

b)Find an approximation for the root of the equation using two bisection method iterations. Tabulate the results.

c) Does your answer have the requested degree of accuracy given above in (a)? Explain.

Answer 1

a)

If x[1,4],

then

f(x)= [-2, 64]

error tolerance, t, = 10^-3

N> log 62 - log 10^-3 /log 8 = 5.30

minimum iterations =6

b)

Using equation;

c)

Yes, the minimum number of iterations will be 6 since it satisfies the equation when x [1,4], and f(x) cannot be a negative