IMO 1966 LL POL35

If a, b, c, d are integers such that ad is odd and bc is even, prove

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IMO 1966 LL POL35

Origin: POL

Problem

If a, b, c, d are integers such that ad is odd and bc is even, prove that at least one root of the polynomial ax3 + bx2 + cx + d is irrational.