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Part of 2018 Ecuador NMO (OMEC)

Problems(1)

p(x)=x^3-24x + k has at most 1 integer root 2018 Ecuador NMO (OMEC) 3.4

Source:

k

be a real number. Show that the polynomial

p (x) = x^3-24x + k

has at most an integer root.

algebrapolynomialinteger roots