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: Employ the Regula Falsi method.
The Regula Falsi method, also known as the False Position method, is an iterative technique for approximating the roots of equations. It uses linear interpolation between two points to estimate the root.For the equation \( f(x) = x^3 + x^2 - 3x - 3 \) within the interval \( [1, 2] \), initial approximations are calculated.Step 2: Implement the formula.
The iterative formula to calculate the next approximation \( x_2 \) is:\[x_2 = \frac{x_1 f(x_2) - x_2 f(x_1)}{f(x_2) - f(x_1)}\]Applying this method, the approximate root is determined to be \( 1.627 \). Final Answer: \[ \boxed{1.627} \]