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Are they correct?

1. "I've to water the plant" OR "I've to watering the plant"

2. "I've watered the plant"
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1. "I've to water the plant" OR "I've to watering the plant"

They're both wrong. You should never contract have to.

I have to water the plant. (ok)

But you can say

I've got to water the plant.

'Have got to' means the same as 'have to' but it's used only in BrE.

2. "I've watered the plant" (ok)

've watered is the contraction for have watered (present perfect) and it's very different from 'have to water'.
Comments  
Students: We have free audio pronunciation exercises.
Very clear explanation. I've learned a lot. Thank you!

I water the plant