Finding the smallest possible value of a in a quadratic.
Numbers a, b and c form an arithmetic sequence if b − a = c − b. Let a, b, c be positive integers forming an arithmetic sequence with a < b < c. Let f(x) = ax^2 + bx + c. Two distinct real numbers r and s satisfy f(r) = s and f(s) = r. If rs = 2017, determine the smallest possible value of a.
The answer is 9.
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