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All roots integers for a polynomial

Source: RMO Maharashtra and Goa 2016, P3

October 11, 2016
number theoryalgebrapolynomial

Problem Statement

Find all integers kk such that all roots of the following polynomial are also integers: f(x)=x3−(k−3)x2−11x+(4k−8).f(x)=x^3-(k-3)x^2-11x+(4k-8).
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