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Suppose the polynomial 

\(f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_2x^2 + a_1x + a_0\)
has integer coefficients, and its roots are distinct integers.

Given that \(a_n=2 \) and \(a_0=66 \), what is the least possible value of \(|a_{n-1}|\)?

 Dec 14, 2019
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The least possible value of |a_{n - 1}| is 26, given by the polynomial 2x^3 - 26x^2 + 38x + 66 = 2(x + 1)(x - 11)(x - 3).

 Dec 14, 2019

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