Practice Case with Repeated Characteristic Roots - 15.2 | 15. Solving Linear Homogeneous Recurrence Equations – Part II | Discrete Mathematics - Vol 2
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge

15.2 - Case with Repeated Characteristic Roots

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define what a characteristic root is.

💡 Hint: Think about how you find sequences related to recurrence.

Question 2

Easy

What happens when the roots of a characteristic equation are repeated?

💡 Hint: Consider the multiplicity of roots.

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 is the first step to solve a linear homogeneous recurrence equation?

  • Define initial conditions
  • Formulate the characteristic equation
  • Substitute values directly

💡 Hint: Think about what helps in understanding sequence patterns.

Question 2

True or false: If characteristic roots are distinct, each root contributes one term to the general solution.

  • True
  • False

💡 Hint: Consider how many times each root appears in forming solutions.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Prove that the general form of the solution for a recurrence relation with one repeated root of multiplicity 3 must include polynomials of degree 2 and how would initial conditions apply?

💡 Hint: Review the relationship between root multiplicities and polynomial degrees.

Question 2

If given a recurrence relation defined by \( a_n = 2a_{n-1} - a_{n-2} \) with first terms as 5 and 6, derive the unique sequence.

💡 Hint: Make sure to set up your equations correctly based on initial values.

Challenge and get performance evaluation