Question

Which of the following numerical methods are used for finding roots of an equation?
(A). Bisection method
(B). Newton-Raphson method
(C). Gaussian elimination method
(D). Regular falsi method

Choose the correct answer from the options given below:

• A. (A), (B) and (C) only.
• B. (B), (C) and (D) only.
• C. (A), (C) and (D).
• D. (A), (B) and (D) only.

Hint:

Be careful to distinguish between single-variable root-finding methods (Bisection, Newton-Raphson, Regular Falsi) and linear system solvers (Gaussian Elimination, LU Decomposition, Gauss-Seidel).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Root-finding algorithms are numerical techniques designed to solve equations of the form \(f(x) = 0\).
These methods iteratively converge to the root starting from an initial guess or bracket.

Step 3: Detailed Explanation:
Let us review the purpose of each listed numerical method:
(A)

Bisection method: A bracketing method used to locate roots of continuous functions.
(B)

Newton-Raphson method: An open, rapid method that uses derivative information to find roots.
(C)

Gaussian elimination method: A systematic matrix reduction process used to solve systems of linear equations, not to locate roots of single equations.
(D)

Regular falsi method: Also known as the false position method, this is a bracketing root-finding method.
Thus, methods (A), (B), and (D) are root-finding methods.

Step 4: Final Answer:
The correct option is 4, which corresponds to (A), (B) and (D) only.