Podcast
Questions and Answers
What is the condition for the equation f(x) = 0 to have at least one real root between a and b?
What is the condition for the equation f(x) = 0 to have at least one real root between a and b?
- f(a) and f(b) have the same sign
- f(a) and f(b) are both positive
- f(a) and f(b) have opposite signs (correct)
- f(a) and f(b) are both negative
What is the graphical method used to find the real roots of an equation?
What is the graphical method used to find the real roots of an equation?
- Plotting the graphs of y = f(x) and y = x
- Plotting the graphs of y = f1(x) and y = f2(x)
- Plotting the graphs of y = f(x) and y = 0
- Plotting the graphs of y = f1(x) and y = f2(x) and finding the points of intersection (correct)
What is the condition for all roots of the equation x^3 - 3x + k = 0 to be real?
What is the condition for all roots of the equation x^3 - 3x + k = 0 to be real?
- k > 2
- k belongs to the range (-2, 2) (correct)
- k belongs to the range [2, 3]
- k < 2
What is the purpose of the Location Theorem in finding the roots of an equation?
What is the purpose of the Location Theorem in finding the roots of an equation?
What is the method of finding the real roots of an equation by plotting the graphs of y = f1(x) and y = f2(x) and finding the abscissae of the points of intersection?
What is the method of finding the real roots of an equation by plotting the graphs of y = f1(x) and y = f2(x) and finding the abscissae of the points of intersection?
When a number is rounded off to n decimal places, what is the maximum bound on the magnitude of relative error?
When a number is rounded off to n decimal places, what is the maximum bound on the magnitude of relative error?
What type of equation is ax^2 + bx + c = 0?
What type of equation is ax^2 + bx + c = 0?
When a number is truncated to n decimal places, what is the maximum bound on the absolute error?
When a number is truncated to n decimal places, what is the maximum bound on the absolute error?
What is the number of significant digits in the number 0.0001?
What is the number of significant digits in the number 0.0001?
What is the absolute error when the number 2.089 is rounded off to three significant digits?
What is the absolute error when the number 2.089 is rounded off to three significant digits?
What is the maximum number of real roots of the equation x²ⁿ - 1 = 0?
What is the maximum number of real roots of the equation x²ⁿ - 1 = 0?
What is the iterative method used for in solving algebraic and transcendental equations?
What is the iterative method used for in solving algebraic and transcendental equations?
What is the condition for all roots of the given equation to be real?
What is the condition for all roots of the given equation to be real?
In the iterative method, what is the value of x₁ if x₀ is the initial approximation to the root α?
In the iterative method, what is the value of x₁ if x₀ is the initial approximation to the root α?
What is the interval in which the smallest positive root of the transcendental equation x - e^x = 0 lies?
What is the interval in which the smallest positive root of the transcendental equation x - e^x = 0 lies?
What is the purpose of the iterative method in solving algebraic and transcendental equations?
What is the purpose of the iterative method in solving algebraic and transcendental equations?
What is the nature of the function g(x) in the iterative method?
What is the nature of the function g(x) in the iterative method?
What is the relationship between the successive approximations x₀, x₁, and x₂ in the iterative method?
What is the relationship between the successive approximations x₀, x₁, and x₂ in the iterative method?
What is the nature of the roots of the equation x²ⁿ - 1 = 0?
What is the nature of the roots of the equation x²ⁿ - 1 = 0?
What is the purpose of locating the root of an equation in the successive bisection method?
What is the purpose of locating the root of an equation in the successive bisection method?
What determines the number of significant digits in a number?
What determines the number of significant digits in a number?
When rounding off a number to n significant digits, what happens to the (n+1)th digit if it is greater than 5?
When rounding off a number to n significant digits, what happens to the (n+1)th digit if it is greater than 5?
What is the purpose of rounding off numbers in numerical methods?
What is the purpose of rounding off numbers in numerical methods?
How many significant digits are in the number 35.9200?
How many significant digits are in the number 35.9200?
What is the rule for rounding off a number to n significant digits if the (n+1)th digit is 5 and is followed by zero or zeros?
What is the rule for rounding off a number to n significant digits if the (n+1)th digit is 5 and is followed by zero or zeros?
What is the characteristic of an algebraic equation?
What is the characteristic of an algebraic equation?
What type of equation is ae^x + b sin x = 0?
What type of equation is ae^x + b sin x = 0?
What is the purpose of the Location Theorem in finding the roots of an equation?
What is the purpose of the Location Theorem in finding the roots of an equation?
What is the iterative method used for in solving algebraic and transcendental equations?
What is the iterative method used for in solving algebraic and transcendental equations?
What is the condition for an equation to have at least one real root between a and b?
What is the condition for an equation to have at least one real root between a and b?
