What is the characteristic equation of a n + 2 + 2 a n =...

Cory Patrick

Cory Patrick

Answered

2022-06-24

What is the characteristic equation of a n + 2 + 2 a n = 0?
So if we let a n = C r n then we have C r n + 2 + 2 C r n = C r n ( r 2 + 2 ). So I got that the characteristic equation r 2 + 2 = 0 but it should be r 2 + 2 r = 0 apparently.

Answer & Explanation

America Barrera

America Barrera

Expert

2022-06-25Added 23 answers

Step 1
The characteristic equation of :
a n + 2 + α a n + 1 + β a n = 0 is:
r 2 + α r + β = 0
Step 2
In your case α = 0 and β = 2.

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