HMMT 2003 U19

Guts
Answer

Let $r, s, t$ be the solutions to the equation $x^{3}+a x^{2}+b x+c=0$ . What is the value of $(r s)^{2}+(s t)^{2}+(r t)^{2}$ in terms of $a, b$ , and $c$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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b^{2}-2 a c

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