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Given that the polynomial x^2 - kx + 18 has only positive integer roots, find the average of all distinct possibilities for k.

 Feb 23, 2021
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18 = 1 * 18, 2 * 9, 3 * 6

 

(x - 1)(x - 18) = x^2 - 19x + 18

(x - 2)(x - 9) = x^2 - 11x + 18

(x - 3)(x - 6) = x^2 - 9x + 18

 

k = 19, 11, 9

 

average: 13

 Feb 23, 2021

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