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2017 preRMO p4, roots (x^2+ax+20)(x^2+17x+b) = 0 are negative integers

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August 9, 2019
trinomialrootsIntegersalgebra

Problem Statement

Let a,ba, b be integers such that all the roots of the equation (x2+ax+20)(x2+17x+b)=0(x^2+ax+20)(x^2+17x+b) = 0 are negative integers. What is the smallest possible value of a+ba + b ?
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