Question

If \( x^2 - x - 4 = 0 \) by bisection method, first two approximations \( x_1 \) and \( x_2 \) are 1 and 2, then \( x_3 \) is

• A. 1.2
• B. 1.3
• C. 1.4
• D. 1.5

Hint:

The bisection method is a numerical method used to find roots of continuous functions by iteratively narrowing the interval where the root lies.

Answer 1

The Correct Option is D

The bisection method is an iterative method used to find the root of a function within a given interval. The method uses the formula:

\[ x_3 = \frac{x_1 + x_2}{2} \]

We are given the function \( f(x) = x^2 - x - 4 \), with the first two approximations \( x_1 = 1 \) and \( x_2 = 2 \).

Step 1: We calculate the value of \( x_3 \) using the bisection method formula:

\[ x_3 = \frac{1 + 2}{2} = 1.5 \]

Thus, the third approximation \( x_3 \) is 1.5, which corresponds to option (D).