5.1.2. Key Concepts

Try these first

1. 1.

   Define an algebraic equation and give an example.

   Hint

   Remember it involves only powers with whole numbers.

2. 2.

   What is the Bisection Method?

   Hint

   Think about how we narrow down the options.

3. 3.

   What type of functions do transcendental equations involve?

   • Polynomial
   • Trigonometric
   • Rational

   Hint

   Think about what transcends polynomial functions.

4. 4.

   True or False: The Bisection Method guarantees finding a root if the function is continuous.

   • True
   • False

   Hint

   Consider the Intermediate Value Theorem.

5. 5.

   You are asked to find the root of the polynomial equation x^3 - 6x^2 + 11x - 6 = 0 using the Bisection Method. Start with the interval [2, 3] and perform two iterations. What is the midpoint after these iterations?

   Hint

   Focus on the calculations of the function values at the midpoints.

6. 6.

   Using the Newton-Raphson Method, find the root of the equation f(x) = x^2 - 2 starting with x0 = 1. What is the value of the root after two iterations?

   Hint

   Apply the formula iteratively and keep track of changes.