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Omni-MATH / Vijay chooses three distinct integers a,b,c from the set {1,2,3,4,5,6,7,8,9,10,11}. If k is the minimum value taken on by the polynomial a(x−b)(x−c) over all real numbers x, and l …

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problem

Vijay chooses three distinct integers a,b,ca, b, c from the set {1,2,3,4,5,6,7,8,9,10,11}\{1,2,3,4,5,6,7,8,9,10,11\}. If kk is the minimum value taken on by the polynomial a(x−b)(x−c)a(x-b)(x-c) over all real numbers xx, and ll is the minimum value taken on by the polynomial a(x−b)(x+c)a(x-b)(x+c) over all real numbers xx, compute the maximum possible value of k−lk-l.
Plain-text mathematical notation (without MathML)
Vijay chooses three distinct integers a,b,c from the set {1,2,3,4,5,6,7,8,9,10,11}. If k is the minimum value taken on by the polynomial a(x−b)(x−c) over all real numbers x, and l is the minimum value taken on by the polynomial a(x−b)(x+c) over all real numbers x, compute the maximum possible value of k−l.
Original LaTeX notation
Vijay chooses three distinct integers \(a, b, c\) from the set \(\{1,2,3,4,5,6,7,8,9,10,11\}\). If \(k\) is the minimum value taken on by the polynomial \(a(x-b)(x-c)\) over all real numbers \(x\), and \(l\) is the minimum value taken on by the polynomial \(a(x-b)(x+c)\) over all real numbers \(x\), compute the maximum possible value of \(k-l\).

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Source and history

task_id
5a4d2102-e259-51b1-8ba2-6a55c0abccbd
task_key
test--5a4d2102-e259-51b1-8ba2-6a55c0abccbd
task_revision_id
1
config / split
/ test

Official source

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