quotient ring confusion

From: Sindy Daley (daleysin_at_hotmail.com)
Date: 12/16/04 

Date: Thu, 16 Dec 2004 01:04:55 +0000 (UTC)

I am trying to get a good grasp as to what this ring
looks like

Z[x]/(x^2-5, 5x-10)

messing with the relations x^2=5 and 5x=10 i get the
additional relation that 2x^2-5x=0. I do not suppose
i could be so lucky as to have that the ideal
(x^2-5,5x-10) is principal, and generated by 2x^2-5x
alone? i feel that if that were the case, then the
quotient ring would be something like the dyadic
rationals Q_2 since we would be adjoining 5/2 to Z.

in any case, i really need to be able to get my head
around the structure in order to understand the rest
of this example from my professor (i am trying to fill
in the missing details).

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