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2 cards from this section. Quick, good the night before a test.
Define characteristic roots.
Think about the roots of a polynomial.
What is a homogeneous recurrence equation?
Consider the structure of terms in the recurrence.
What does the general form of a solution involve when roots are distinct?
Think of the structure provided from roots.
True or False: Repeated roots do not influence the solution's structure.
Reflect on the earlier discussion about root multiplicity.
For the recurrence relation T_n = T_{n-1} + T_{n-2}, identify the roots and derive the general solution.
Start with the characteristic polynomial and factor it.
Given T_n = 2 T_{n-1} + T_{n-2} with the initial conditions T_0 = 1 and T_1 = 2, find T_n for n = 5.
Work through the constants based on initial value equations.
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