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I have the following question which i'm not sure how to work out...

$For\ f=6x^2y-xy^2-2y^3+1\ and\ \ h=3x-2y\ \in \mathbb{C}[x,y]$

Show that V(f,h) is empty.

What can you say about the ideal (f,h)?

I'm really not sure how I go about answering these questions.. any help would be greatly appreciated!!

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Here is a hint:

Note that f can be written as f=1+(3x-2y)(2x+y)y

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  • $\begingroup$ Im just not sure how you actually go about showing whether a variety is empty or not.. $\endgroup$ Commented Mar 12, 2013 at 13:54

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