# MATH / 

task_id: 9690f309-00fc-52ab-bb76-337c71d63fc5
task_key: intermediate~5falgebra--test--9690f309-00fc-52ab-bb76-337c71d63fc5
task_revision_id: 1

{"level":"Level 5","problem":"Let $r_1,$ $r_2,$ $\\dots,$ $r_7$ be the distinct complex roots of the polynomial $P(x) = x^7 - 7.$  Let\n\\[K = \\prod_{1 \\le i < j \\le 7} (r_i + r_j).\\]In other words, $K$ is the product of all numbers of the of the form $r_i + r_j,$ where $i$ and $j$ are integers for which $1 \\le i < j \\le 7.$  Determine $K^2.$","type":"Intermediate Algebra"}

Source: https://github.com/hendrycks/math

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