Question

c) Use the Bisection method to find a solution accurate to within 10^-2 for x^4 − 2x^3 − 4x^2 + 4x + 4 = 0 on [0, 2].

Answer 1

Answer:

  x ≈ 181/128 ≈ 1.41406

Step-by-step explanation:

The attached table shows the iterations. At each step, the interval containing the root is bisected and the function value at the midpoint of the interval is found. The sign of it relative to the signs of the function values at the ends of the interval tell which half interval contains the root. The process is repeated until the interval width is less than 10^-2.

Interval: [0, 2], signs [+, -], midpoint: 1; sign at midpoint: +

             [1, 2]                                      3/2                           -

             [1, 3/2]                                   5/4                           +

...

the rest is in the attachment. The listed table values are the successive interval midpoints.

The final midpoint is 181/128 ≈ 1.41406. This is within 0.0002 of the actual root.

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The actual solution in the interval [0, 2] is √2 ≈ 1.41421.