Question 1074883
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The symmetry axis for this parabola is x = 6, for any value of k.


Therefore, for any value of k, the roots are equidistant from the point x = 6.


Since we are looking for integer positive roots, we can have only these pairs:

(5,7)

(4,8)

(3,9)

(2,10)

(1,11)


Of them, only the pair (5,7) satisfies the given condition.


<U>Answer</U>.  Only the pair (5,7) satisfies the given condition, which gives k = 5*7 = 35.
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