# Prime Cubic Root

Algebra Level pending

Consider the general cubic polynomial with nonzero integer coefficients and constant term, namely, $$f(x) = ax^3 +bx^2 +cx +d$$, where $$a>1$$ is prime, $$|d|>1$$ is prime, and $$f(1) = 1+d$$. From the given info above, $$c = 1-a-b$$. Find another expression of $$c$$ that proves $$f(x)$$ has exactly one rational root.

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