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Given that the polynomial x^2 - 15x + t = 0 has only positive integer roots, find the average of all distinct possible values of t.

 Aug 1, 2022
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The roots of the quadratic are \({15 \pm \sqrt{225-4t} \over 2}\)

 

Note that \(\sqrt {225 - 4t}\) must be an odd, positive integer. 

 

To solve, set \(\sqrt{225 - 4t}\) equal to 13, 11, 9, 7, 5, 3, and 1.

 

Now, solve for t in all cases and find the average.

 Aug 2, 2022

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