Practice Example with Degree 2 Characteristic Equations - 15.5 | 15. Solving Linear Homogeneous Recurrence Equations – Part II | Discrete Mathematics - Vol 2
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15.5 - Example with Degree 2 Characteristic Equations

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the characteristic equation of the recurrence relation f(n) = 6f(n-1) + 9f(n-2)?

💡 Hint: Write the characteristic equation based on the recurrence relation.

Question 2

Easy

Define what initial conditions are in the context of recurrence relations.

💡 Hint: Think about how initial values are used in calculations.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What happens to the general solution if the roots of the characteristic equation are repeated?

  • It remains unchanged.
  • It becomes a polynomial multiplied by the root raised to its multiplicity.
  • It is impossible to determine
  • It simplifies to a linear function.

💡 Hint: Recall the form of solutions for distinct versus repeated roots.

Question 2

True or False: Initial conditions can be ignored when finding general solutions from characteristic equations.

  • True
  • False

💡 Hint: Consider the role of initial conditions in solving recurrence relations.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given the recurrence relation f(n) = 2f(n-1) + f(n-2) with initial conditions f(0)=1 and f(1)=2, find the general solution.

💡 Hint: Don't forget to check the nature of the roots before proceeding with initial conditions.

Question 2

Determine the general form of the recurrence relation defined by f(n) = 4f(n-1) - 4f(n-2) with no initial conditions.

💡 Hint: Focus on the given recurrence structure to create the characteristic equation first.

Challenge and get performance evaluation