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2022 SSMO Accuracy Round Problems/Problem 4

Revision as of 13:03, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== A monic polynomial <math>f</math> has real roots <math>r,s,t.</math> A monic polynomial <math>g</math> has roots <math>r^3,s^3,t^3.</math> Given that the minimum p...")
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Problem

A monic polynomial $f$ has real roots $r,s,t.$ A monic polynomial $g$ has roots $r^3,s^3,t^3.$ Given that the minimum possible value of $\frac{g(1)}{f(1)}$ is $\frac{m}{n},$ for relatively prime positive integers $m$ and $n,$ find $m+n.$

Solution

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