Find n for which the nth iteration by the bisection method guarantees to approximate the root of f(x) = 2x^2 − 3x − 2 on [−2, 1] with accuracy within 10^−8 .

n = 29 iterations would be enough to obtain a root of that is at most away from the correct solution.

Step-by-step explanation:

You can use this formula which relates the number of iterations, n, required by the bisection method to converge to within an absolute error tolerance of ε starting from the initial interval (a, b).

We know

a = -2, b = 1 and ε = so

Thus, n = 29 iterations would be enough to obtain a root of that is at most away from the correct solution.

You can prove this result by doing the computation as follows:

From the information given we know:

This is the algorithm for the Bisection method:

We know that and so we take and then

Because we set as the new b.

The bisection algorithm is detailed in the following table.

After the 29 steps we have that hence the required root approximation is c = -0.50

if im not mistaking its

step-by-step explanation: