Is write trondamere and not tryndamere

Next to that Doran's Ring is superior to Doran's Shield!

Yea sure, but CDR from Athene's and the mana flow is far more useful than the health from Rod. There's also no ramp up. Zyra doesn't need to be beefy, she just needs to lay down CC to peel and blow people up with her 40% CDR from Athenes and her W. She's not Swain or some other aggro mage who would actually benefit from Rod.

I thought so too, then i tried it and it works, provides more ability power than Athene's, and more survive-ability. More hits you can take, the less you break.

Rod of Ages is a terrible first item for zyra. She doesn't need the mana and HP at all. It's much better to get raw power in the form of Athene's and possibly Liandry's.