Given that the polynomial $x^2-5x+t$ has only positive integer roots, find the average of all distinct possible values of $t$.
Question:
Given that the polynomial $x^2-5x+t$ has only positive integer roots, find the average of all distinct possible values of $t$.
Answer:
Let's think step by step.

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Given that the polynomial $x^2-5x+t$ has only positive integer roots, find the average of all distinct possible values of $t$.
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