I have registered my ledger with the tezos root key. I've seen that this is not recommended.
Why it is not recommended and what are the risks of doing that?
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I believe the root key refers to the master key of a hierarchical deterministic (HD) hardware wallet, from which all the keys of the wallet for any supported cryptocurrency are derived (BIP-32).
The BIP32 specification was developed so that:
wallets [...] can be shared partially or entirely with different systems, each with or without the ability to spend coins (source).
As Obsidian Systems states, all Tezos BIP32 paths begin with 44'/1729', and when you generate a wallet with Ledger and do not change anything, the wallet will be generated on path 44'/1729'/0'/0' (which is the standard path for Tezos, not the root).
I think what they say is that they do not recommend to use the master key from which all your keys are derived, because if this key is ever compromised (although unlikely as you are using a hardware wallet), it would open up the door to your wealth. But if you do not change anything during wallet generation, the correct path is used anyway and you are fine.