# Roots of a cubic polynomial

Number Theory Level pending

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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