Characteristic Root Technique

In this example we solve a recurrence relation (with initial conditions) using the famed characteristic root technique

[BillerKee]

You're a legend for making this so clear and concise. Simple, straightforward steps that are easy to understand. If you're still out there, know that you saved another soul from being crushed by a discrete math midterm.

[impstuff]

Best resource I've found on this topic, clear, concise, and covers everything. Thank you

[alajlan]

this is the best explanation had been uploaded on youtube EVER

[kkamous]

Alots of thanks dear, , , ,
You solve my problem, , ,
May Allah bless you

[xiaoying]

thank you so much! I was so lost reading the long paragraph in my notes and you explained it so clearly!!

[gabriel-ocpt]

It finally clicked together thank you!

[cfltd.]

It's 6am and I can't sleep, so now I'm here, for no real reason

[alex_turing]

Where can I find a proof or explanation of why the technique works

[rapid_xcrement]

jump scare at 3:05, great video but that sound really caught me off guard.

[hirakmondal]

*_He has not shown the case where 2 roots are equal_*
Say for this equation -->> an - 4(an -1) + 4 an-2=0
In this case our roots will be equal, that is we will get 2, 2 as our roots..
*_For this case we have a different equation_* --> an=c1(root 1)^n + c2 n (root 2)^n

So for the above given equation the ans will be--->> an = c1 (2)^n + c2 n (2)^n

[shafikbarah]

How can we do
A n = 2A n-¹ _ A n-²
When A¹ = 0 and A² = 62

[savannahpleau]

thank you so much! this was very clear. I appreciate it!

[ShazNoman]

Thanks for explaining.👍👍
Very informative video!

[leoniduvarov]

Thank you so much for this explanation

[Wezla]

exceptionally helpful, cause I followed perfectly without sound

[ナルクロロ]

Damn this is the easiest one i've ever found on ch. roots

[jessstuart]

2:20 I was looking for a derivation, not a cookbook formula. Not helpful.