{"id":1809,"date":"2024-10-08T17:25:27","date_gmt":"2024-10-08T17:25:27","guid":{"rendered":"https:\/\/gbelentzas.sites.sch.gr\/?p=1809"},"modified":"2024-10-11T10:57:40","modified_gmt":"2024-10-11T10:57:40","slug":"1-3-%cf%80%ce%bf%ce%bb%cf%85%cf%8e%ce%bd%cf%85%ce%bc%ce%b1-%ce%af%cf%83%ce%b1-%cf%80%ce%bf%ce%bb%cf%85%cf%8e%ce%bd%cf%85%ce%bc%ce%b1","status":"publish","type":"post","link":"https:\/\/gbelentzas.sites.sch.gr\/?p=1809","title":{"rendered":"1.3 \u03a0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03b1 – \u038a\u03c3\u03b1 \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03b1"},"content":{"rendered":"

<\/i> \u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2<\/i><\/b><\/span><\/h4>\n

\u0394\u03cd\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03b1<\/strong>, \u03cc\u03c4\u03b1\u03bd \u03ad\u03c7\u03bf\u03c5\u03bd \u03cc\u03c1\u03bf\u03c5\u03c2 \u03af\u03c3\u03b1 \u03bc\u03bf\u03bd\u03ce\u03bd\u03c5\u03bc\u03b1.<\/em><\/span><\/p>\n

\u0393\u03b9\u03b1 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b4\u03cd\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03b1 \u03af\u03c3\u03b1, \u03b8\u03b1 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bf\u03b9 \u03b1\u03bd\u03c4\u03af\u03c3\u03c4\u03bf\u03b9\u03c7\u03bf\u03b9 \u03cc\u03c1\u03bf\u03b9 \u03c4\u03bf\u03c5\u03c2 (\u03cc\u03c1\u03bf\u03b9 \u03bc\u03b5 \u03af\u03b4\u03b9\u03b5\u03c2 \u03b4\u03c5\u03bd\u03ac\u03bc\u03b5\u03b9\u03c2 \u03c4\u03b7\u03c2 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ae\u03c2) \u03bd\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bd \u03c4\u03bf\u03c5\u03c2 \u03af\u03b4\u03b9\u03bf\u03c5\u03c2 \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ad\u03c2. \u0391\u03c5\u03c4\u03cc \u03bc\u03b1\u03c2 \u03bf\u03b4\u03b7\u03b3\u03b5\u03af \u03c3\u03c4\u03b7 \u03c3\u03cd\u03b3\u03ba\u03c1\u03b9\u03c3\u03b7 \u03c4\u03c9\u03bd \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ce\u03bd \u03b1\u03c5\u03c4\u03ce\u03bd \u03c4\u03c9\u03bd \u03cc\u03c1\u03c9\u03bd, \u03ba\u03ac\u03c4\u03b9 \u03c0\u03bf\u03c5 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03ba\u03b1\u03c4\u03b1\u03bb\u03ae\u03be\u03b5\u03b9 \u03c3\u03b5 \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5 \u03b2\u03b1\u03b8\u03bc\u03bf\u03cd \u03b3\u03b9\u03b1 \u03c4\u03b9\u03c2 \u03ac\u03b3\u03bd\u03c9\u03c3\u03c4\u03b5\u03c2 \u03c0\u03b1\u03c1\u03b1\u03bc\u03ad\u03c4\u03c1\u03bf\u03c5\u03c2.<\/p>\n

\u0391\u03c2 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03bc\u03b9\u03b1 \u03b2\u03b1\u03c3\u03b9\u03ba\u03ae \u03ac\u03c3\u03ba\u03b7\u03c3\u03b7 \u03b5\u03cd\u03c1\u03b5\u03c3\u03b7\u03c2 \u03c4\u03c9\u03bd \u03c4\u03b9\u03bc\u03ce\u03bd \u03ac\u03b3\u03bd\u03c9\u03c3\u03c4\u03c9\u03bd \u03c0\u03b1\u03c1\u03b1\u03bc\u03ad\u03c4\u03c1\u03c9\u03bd \u03ce\u03c3\u03c4\u03b5 \u03b4\u03cd\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03b1 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03b1.<\/p>\n

\u03a0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1.<\/span><\/strong><\/em> \u0394\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf\u00a0 <\/span>\u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf \"P(x) = 4x^2 - 8x + \alpha x^3 - 5.\" \u0391\u03bd \u03c4\u03bf P(x) \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03bf \u03bc\u03b5 \u03c4\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf \"Q(x) = \beta x^2 + \gamma x + \delta,\" \u03c0\u03bf\u03b9\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \u03b1, \u03b2, \u03b3, \u03b4;<\/p>\n

    \n
  • \u0392\u03ae\u03bc\u03b1 1\u03bf:<\/strong> \u0393\u03b9\u03b1 \u03bd\u03b1 \u03bb\u03cd\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7\u03bd \u03ac\u03c3\u03ba\u03b7\u03c3\u03b7 \u03bc\u03b5 \u03c3\u03c9\u03c3\u03c4\u03cc \u03c4\u03c1\u03cc\u03c0\u03bf, \u03c4\u03bf \u03c0\u03c1\u03ce\u03c4\u03bf \u03b2\u03ae\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bd\u03b1 \u03b3\u03c1\u03ac\u03c8\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b1 \u03b4\u03cd\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03b1 \u03ba\u03b1\u03c4\u03ac \u03c6\u03b8\u03af\u03bd\u03bf\u03c5\u03c3\u03b1 \u03c3\u03b5\u03b9\u03c1\u03ac \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03b9\u03c2 \u03b4\u03c5\u03bd\u03ac\u03bc\u03b5\u03b9\u03c2 \u03c4\u03bf\u03c5 .<\/li>\n<\/ul>\n

    \u03a4\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf\u00a0 \"P(x)\" \u00a0<\/span>\u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03b3\u03c1\u03b1\u03bc\u03bc\u03ad\u03bd\u03bf \u03ba\u03b1\u03c4\u03ac \u03c6\u03b8\u03af\u03bd\u03bf\u03c5\u03c3\u03b1 \u03c3\u03b5\u03b9\u03c1\u03ac \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03bf x. T\u03bf \u03b1\u03bd\u03b1\u03b4\u03b9\u03b1\u03c4\u03ac\u03c3\u03c3\u03bf\u03c5\u03bc\u03b5 \u00a0\u03ba\u03b1\u03b9 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 :<\/p>\n

      <\/span>   <\/span>\"\[P(x) = \alpha x^3 + 4x^2 - 8x - 5\]\"<\/p>\n<\/p>\n

    \u03a4\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf\u00a0 \"Q(x)\" <\/span>\u03b5\u03af\u03bd\u03b1\u03b9 \u03ae\u03b4\u03b7 \u03b3\u03c1\u03b1\u03bc\u03bc\u03ad\u03bd\u03bf \u03ba\u03b1\u03c4\u03ac \u03c6\u03b8\u03af\u03bd\u03bf\u03c5\u03c3\u03b1 \u03c3\u03b5\u03b9\u03c1\u03ac \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03b9\u03c2 \u03b4\u03c5\u03bd\u03ac\u03bc\u03b5\u03b9\u03c2 \u03c4\u03bf\u03c5 x.<\/p>\n

      \n
    • B\u03ae\u03bc\u03b1 2\u03bf:<\/strong> \u03a3\u03cd\u03b3\u03ba\u03c1\u03b9\u03c3\u03b7 \u03c4\u03c9\u03bd \u03cc\u03bc\u03bf\u03b9\u03c9\u03bd \u03cc\u03c1\u03c9\u03bd\n
        \n
      • \u03a3\u03cd\u03b3\u03ba\u03c1\u03b9\u03c3\u03b7 \u03c4\u03c9\u03bd \u03cc\u03c1\u03c9\u03bd \u03bc\u03b5 \"x^3\"<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

        \u03a3\u03c4\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf \"P(x)\" \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03bf \u03cc\u03c1\u03bf\u03c2 \"\alpha x^3\" , \u03b1\u03bb\u03bb\u03ac \u03c3\u03c4\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf \"Q(x)\" \u03b4\u03b5\u03bd \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03cc\u03c1\u03bf\u03c2 \u03bc\u03b5 \"x^3\" . \u0393\u03b9\u03b1 \u03c4\u03b1 \u03b4\u03cd\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03b1 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03b1, \u03b1\u03c5\u03c4\u03cc \u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03bf \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ae\u03c2 \"\alpha=0\"<\/p>\n

          \n
        • \n
            \n
          • \u00a0\u03a3\u03cd\u03b3\u03ba\u03c1\u03b9\u03c3\u03b7 \u03cc\u03c1\u03c9\u03bd \u03bc\u03b5 \"x^2\"<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

            \u039f \u03cc\u03c1\u03bf\u03c2 \u03bc\u03b5 \u03ba\u03cd\u03c1\u03b9\u03bf \u03bc\u03ad\u03c1\u03bf\u03c2 \u00a0\"x^2\" \u03c3\u03c4\u03bf \"P(x)\" \u03b5\u03af\u03bd\u03b1\u03b9 \"4x^2\", \u03b5\u03bd\u03ce \u03c3\u03c4\u03bf \"Q(x)\" \u03b5\u03af\u03bd\u03b1\u03b9 \"\beta x^2\" . \u03a3\u03c5\u03bd\u03b5\u03c0\u03ce\u03c2, \u03bf\u03b9 \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ad\u03c2 \u03c4\u03c9\u03bd \u03cc\u03c1\u03c9\u03bd \u03bc\u03b5 \"x^2\" \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03bf\u03b9, \u03ac\u03c1\u03b1: \u00a0\"\beta = 4\"<\/p>\n

              \n
            • \n
                \n
              • \u00a0\u03a3\u03cd\u03b3\u03ba\u03c1\u03b9\u03c3\u03b7 \u03cc\u03c1\u03c9\u03bd \u03bc\u03b5 x<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

                \u039f \u03cc\u03c1\u03bf\u03c2 \u03bc\u03b5 \"x\" \u03c3\u03c4\u03bf \"P(x)\" \u03b5\u03af\u03bd\u03b1\u03b9 \"-8x\" , \u03b5\u03bd\u03ce \u03c3\u03c4\u03bf \"Q(x)\" \u03b5\u03af\u03bd\u03b1\u03b9 \"\gamma x\". \u03a3\u03c5\u03bd\u03b5\u03c0\u03ce\u03c2, \u03bf\u03b9 \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ad\u03c2 \u03c4\u03c9\u03bd \u03cc\u03c1\u03c9\u03bd \u03bc\u03b5 x \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03bf\u03b9, \u03ac\u03c1\u03b1: \"\gamma = -8\"<\/p>\n

                  \n
                • \n
                    \n
                  • \u03a3\u03cd\u03b3\u03ba\u03c1\u03b9\u03c3\u03b7 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ce\u03bd \u03cc\u03c1\u03c9\u03bd<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

                    \u039f \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03cc\u03c2 \u03cc\u03c1\u03bf\u03c2 \u03c3\u03c4\u03bf \"P(x)\" \u03b5\u03af\u03bd\u03b1\u03b9 \"-5\", \u03b5\u03bd\u03ce \u03c3\u03c4\u03bf \"Q(x)\" \u03b5\u03af\u03bd\u03b1\u03b9 \"\delta\". \u03a3\u03c5\u03bd\u03b5\u03c0\u03ce\u03c2, \u03bf\u03b9 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03bf\u03af \u03cc\u03c1\u03bf\u03b9 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03bf\u03b9, \u03ac\u03c1\u03b1: \"\delta = -5\"<\/p>\n

                    \u0395\u03c0\u03bf\u03bc\u03ad\u03bd\u03c9\u03c2, \u00a0\u03bf\u03b9 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \u03c0\u03b1\u03c1\u03b1\u03bc\u03ad\u03c4\u03c1\u03c9\u03bd \u03b5\u03af\u03bd\u03b1\u03b9: \"\alpha = 0, \, \beta = 4, \, \gamma = -8, \, \delta = -5\"<\/p>\n

                    \n

                    <\/i> <\/i><\/b>Let’s Practise<\/b><\/span><\/h4>\n

                    \u0386\u03c3\u03ba\u03b7\u03c3\u03b7 1<\/strong><\/p>\n

                    \u0394\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf \"P(x) = 3x^2 + 2\alpha x + 2\" \u03ba\u03b1\u03b9 \u03c4\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf \"Q(x) = (\beta +1)x^2 + (\alpha - 4)x + 5\". \u0391\u03bd \u03c4\u03b1 \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03b1 \u03b1\u03c5\u03c4\u03ac \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03b1, \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \"\alpha\" \u03ba\u03b1\u03b9 \"\beta\" .<\/p>\n

                    \u0386\u03c3\u03ba\u03b7\u03c3\u03b7 2<\/strong><\/p>\n

                    \u0394\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf \"P(x) = (3\alpha - 2)x^2 - 3x + 7\" \u03ba\u03b1\u03b9 \u03c4\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03bf \"Q(x) = (\gamma -2)x^3 + x^2 - 3x + (\beta + 1).\" \u0391\u03bd \u03c4\u03b1 \u03b4\u03cd\u03bf \u03c0\u03bf\u03bb\u03c5\u03ce\u03bd\u03c5\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03b1, \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \"\alpha, \, \beta\" \u00a0 \u03ba\u03b1\u03b9 \"\gamma.\"<\/p>\n

                    \n

                    \u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1:<\/strong> \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u0393 \u0393\u03c5\u03bc\u03bd\u03b1\u03c3\u03af\u03bf\u03c5 (\u0394\u03b7\u03bc\u03ae\u03c4\u03c1\u03b9\u03bf\u03c2 \u0391\u03c1\u03b3\u03c5\u03c1\u03ac\u03ba\u03b7\u03c2 , \u03a0\u03b1\u03bd\u03b1\u03b3\u03b9\u03ce\u03c4\u03b7\u03c2 \u0392\u03bf\u03c5\u03c1\u03b3\u03ac\u03bd\u03b1\u03c2, \u039a\u03c9\u03bd\u03c3\u03c4\u03b1\u03bd\u03c4\u03af\u03bd\u03bf\u03c2 \u039c\u03b5\u03bd\u03c4\u03ae\u03c2, \u03a3\u03c4\u03b1\u03bc\u03b1\u03c4\u03bf\u03cd\u03bb\u03b1 \u03a4\u03c3\u03b9\u03ba\u03bf\u03c0\u03bf\u03cd\u03bb\u03bf\u03c5, \u039c\u03b9\u03c7\u03b1\u03ae\u03bb \u03a7\u03c1\u03c5\u03c3\u03bf\u03b2\u03ad\u03c1\u03b3\u03b7\u03c2 \u03a5.\u03a0\u0391\u0399.\u0398.)<\/p>\n

                    Creative Commons \u0391\u03bd\u03b1\u03c6\u03bf\u03c1\u03ac \u0394\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03bf\u03cd – \u039c\u03b7 \u0395\u03bc\u03c0\u03bf\u03c1\u03b9\u03ba\u03ae \u03a7\u03c1\u03ae\u03c3\u03b7 – \u03a0\u03b1\u03c1\u03cc\u03bc\u03bf\u03b9\u03b1 \u0394\u03b9\u03b1\u03bd\u03bf\u03bc\u03ae 4.0 \u0394\u03b9\u03b5\u03b8\u03bd\u03ad\u03c2<\/strong><\/p>\n

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