MathDB
CIIM 2018 Problem 4

Source:

March 10, 2019
CIIM2018undergraduate

Problem Statement

Let α<0<β\alpha < 0 < \beta and consider the polynomial f(x)=x(x−α)(x−β)f(x) = x(x-\alpha)(x-\beta). Let SS be the set of real numbers ss such that f(x)−sf(x) - s has three different real roots. For s∈Ss\in S, let p(x)p(x) the product of the smallest and largest root of f(x)−sf(x)-s. Determine the smallest possible value that p(s)p(s) for s∈Ss\in S.
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