{
  "icon" : "function",
  "id" : "704BC483-E05E-55AB-9159-2EBB0B3D8435",
  "lines" : [
    {
      "id" : "F4BC83AF-5B4C-5DC3-B6F8-F1398ED3AB60",
      "source" : "# Roots by factoring"
    },
    {
      "id" : "CF23CA2A-9907-5234-988D-99BC0F03CE15",
      "source" : "solve(x²-5*x+6, x)"
    },
    {
      "id" : "F22AE7CA-5090-572C-B313-04EAADA59E9C",
      "source" : "factor(x²-5*x+6, x)"
    },
    {
      "id" : "6B1A188C-2AFF-547E-BC83-FA9B5365A95D",
      "source" : "solve(x²+7*x+12, x)"
    },
    {
      "id" : "3312CBE1-AD25-53C3-9107-2772B334A70C",
      "source" : ""
    },
    {
      "id" : "79CED821-A33C-5A28-A248-138E7D88A042",
      "source" : "# A cubic"
    },
    {
      "id" : "01A4296A-442B-55C3-A991-DBF84D3CC3E6",
      "source" : "p(x) = x³-6*x²+11*x-6"
    },
    {
      "id" : "F66B80AB-0DB5-5B28-B192-F4FD79CD8F72",
      "source" : "factor(p(x), x)"
    },
    {
      "id" : "4A76517D-169A-57F4-B5CF-5E4DF646CBFD",
      "source" : "\/\/ Each root makes the cubic zero."
    },
    {
      "id" : "5F881202-6255-52E6-AA28-5F9694DF4D84",
      "source" : "p(1) == 0 and p(2) == 0 and p(3) == 0"
    },
    {
      "id" : "C4D5F085-CBBB-52F2-8B85-938E99909D8E",
      "source" : ""
    },
    {
      "id" : "B2B0DDC0-1F90-5B06-8989-1F5C9AB759E4",
      "source" : "# Sum and product of roots"
    },
    {
      "id" : "C87085EA-98C9-5240-A449-711912AC3E5F",
      "source" : "\/\/ For ax² + bx + c, roots sum to -b\/a and multiply to c\/a. Here x² - 5x + 6."
    },
    {
      "id" : "94BD845F-83FE-5CE1-BE3A-3326CC0F1A50",
      "source" : "a = 1"
    },
    {
      "id" : "FD1B2546-232C-5DF7-A704-E8959382B45E",
      "source" : "b = -5"
    },
    {
      "id" : "34C91452-FA33-5271-B15D-01E29ACB9DE8",
      "source" : "c = 6"
    },
    {
      "id" : "8550D2B8-A1DA-5344-804A-C975DB46348F",
      "source" : "root sum = -b\/a"
    },
    {
      "id" : "1DDDED6D-C7BD-5361-8557-F81B9BA37CC2",
      "source" : "root sum == 2 + 3"
    },
    {
      "id" : "96572952-EF18-5085-8324-BD013E71D4C8",
      "source" : "root product = c\/a"
    },
    {
      "id" : "616175DB-CFBE-5BE0-9BE7-EDE660B07210",
      "source" : "root product == 2*3"
    }
  ],
  "numberStyle" : {
    "decimal" : ".",
    "grouping" : ",",
    "secondaryGroupSize" : 3
  },
  "title" : "Polynomial roots"
}