# A Rational Cubic with Imaginary Entry Point

Algebra Level pending

Consider the cubic integer polynomial $$h(x)=3x^3+a_2x^2+a_1x+a_0$$ given prime $$|a_0|>15$$ and where $$h(1)=12$$. Find $$a_0$$ such that $$h(x)$$ has one rational root and two complex roots.

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