Question

Find a real root of x^3-3x+1=0 using bisection method correct to two decimal places.​

Answer 1

Answer:

To achieve accuracy up to two decimal places means the error between the real root and numerically calculated root should be less than 0.01

⇒ ϵ < 0.01

f(x) = x3 – x – 1, 1 ≤ x ≤ 2

Accuracy (ε) = 0.01

Accuracy of bisection method is given by,

⇒ 2n ≥ 100

Now 26 = 64, 27 = 128

∴ Minimum number of n to satisfy the above condition is, n = 7