HMMT 2004 U25

Guts
Answer

Suppose $x^{3}-a x^{2}+b x-48$ is a polynomial with three positive roots $p, q$ , and $r$ such that $p<q<r$ . What is the minimum possible value of $1 / p+2 / q+3 / r$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3}{2}

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