C++ Root-Finding Methods Quiz

In the Bisection method C++ program, what is the condition to stop iteration?

• Iteration count exceeds limit

• f(c) becomes zero

• Interval becomes less than tolerance

• All of the above

Which header file is essential for mathematical functions like fabs() in C++?

• iostream

• stdio.h

• math.h

• conio.h

What does the function f(x) typically represent in these programs?

• Iteration limit

• Derivative function

• User-defined function

• Main program

Which variable holds the midpoint in the Bisection method?

• x0

• x1

• x

• c

In the method of False Position, how is the next approximation calculated?

• Midpoint of interval

• Intersection of line joining endpoints

• Derivative evaluation

• Successive value

What is the general form of Newton-Raphson’s formula in code?

• x1 = x0 - f(x0)

• x1 = x0 + f(x0)/f'(x0)

• x1 = x0 - f(x0)/f'(x0)

• x1 = x0 * f'(x0)

In Successive Approximation, the function must be written as:

• f(x) = 0

• x = g(x)

• x² = 0

• f'(x) = 0

Which loop is mostly used in root-finding C++ programs?

• for loop

• while loop

• do-while loop

• nested loop

What is the return type of f(double x) function usually?

• int

• void

• float

• double

What is a key drawback of Newton-Raphson in C++ implementation?

• Slow convergence

• Requires derivative

• Needs interval

• Doesn't work in C++