Consider the cubic polynomial

\[\large p(x)=ax^3+ bx^2 + cx + d\]

where \(a\), \(b\), \(c\), and \(d\) are integers such that \(ad\) is odd and \(bc\) is even and not all roots of \(p(x)\) can be rational.

Is this **possible**? If yes, prove it. If no, why?

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