Question

Using the method of Regula Falsi, a root of the equation \( x^3 + x^2 - 3x - 3 = 0 \) lying between 1 and 2 is

• A. 1.627
• B. 1.728
• C. 1.023
• D. 1.975

Hint:

In the Regula Falsi method, always iterate between two points where the function changes sign.

Answer 1

The Correct Option is A

Step 1: Use the Regula Falsi method.
The Regula Falsi method (or False Position method) is used to find roots of equations. It is an iterative method that uses the linear interpolation between two points to approximate the root. Given the equation \( f(x) = x^3 + x^2 - 3x - 3 \) and the interval \( [1, 2] \), we calculate the initial approximations. Step 2: Apply the formula.
The formula for the next approximation \( x_2 \) is: \[ x_2 = \frac{x_1 f(x_2) - x_2 f(x_1)}{f(x_2) - f(x_1)} \] Using the method, we find that the root is approximately \( 1.627 \). Final Answer: \[ \boxed{1.627} \]