{"id":28841,"date":"2021-03-30T13:00:35","date_gmt":"2021-03-30T13:00:35","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28841"},"modified":"2024-09-22T02:06:07","modified_gmt":"2024-09-22T02:06:07","slug":"%d1%84%d0%b0%d0%ba%d1%82%d0%be%d1%80%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d1%8f-%d0%ba%d0%b2%d0%b0%d0%b4%d1%80%d0%b0%d1%82%d0%bd%d0%be%d0%b3%d0%be-%d0%b8-2n-%d0%ba%d0%b2%d0%b0%d0%b4%d1%80%d0%b0%d1%82%d0%bd","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ru\/%d1%84%d0%b0%d0%ba%d1%82%d0%be%d1%80%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d1%8f-%d0%ba%d0%b2%d0%b0%d0%b4%d1%80%d0%b0%d1%82%d0%bd%d0%be%d0%b3%d0%be-%d0%b8-2n-%d0%ba%d0%b2%d0%b0%d0%b4%d1%80%d0%b0%d1%82%d0%bd\/","title":{"rendered":"\u0424\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0438 2n-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0424\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0438 2n-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430<\/h1>\n<p><em><strong>\u0420\u0435\u0437\u044e\u043c\u0435:<\/strong><br \/>\n   \u041d\u0430 \u044d\u0442\u043e\u043c \u0437\u0430\u043d\u044f\u0442\u0438\u0438 \u043c\u044b \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^2 + bx + c<\/span> \u0438 2n-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 <span class=\"katex-eq\" data-katex-display=\"false\">(2n)<\/span>-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2n} + bx^n + c<\/span>, \u0440\u0430\u0441\u043a\u043b\u0430\u0434\u044b\u0432\u0430\u044f \u0438\u0445 \u043d\u0430 \u043f\u0440\u043e\u0441\u0442\u044b\u0435 \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u0438. \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0431\u0443\u0434\u0443\u0442 \u043f\u0440\u043e\u0440\u0430\u0431\u043e\u0442\u0430\u043d\u044b \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u044b \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b.<\/em><\/p>\n<p>   <strong>\u0426\u0435\u043b\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f<\/strong><\/p>\n<ol style=\"text-align: left;\">\n<li><strong>\u041d\u0430\u0443\u0447\u0438\u0442\u044c\u0441\u044f<\/strong> \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u0432\u0438\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^2 + bx + c<\/span>.<\/li>\n<li><strong>\u0412\u044b\u0432\u0435\u0441\u0442\u0438<\/strong> \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 <span class=\"katex-eq\" data-katex-display=\"false\">x = \\displaystyle \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}<\/span> \u0434\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043a\u043e\u0440\u043d\u0435\u0439.<\/li>\n<li><strong>\u041f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c<\/strong> \u043c\u0435\u0442\u043e\u0434\u044b \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u043a (2n)-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u043c \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430\u043c \u0432\u0438\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2n} + bx^n + c<\/span>.<\/li>\n<li><strong>\u0420\u0430\u0441\u043f\u043e\u0437\u043d\u0430\u0432\u0430\u0442\u044c<\/strong> \u0443\u0441\u043b\u043e\u0432\u0438\u044f, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0435 \u0434\u043b\u044f \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432.<\/li>\n<li><strong>\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c<\/strong> \u043c\u0435\u0442\u043e\u0434 \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0430 \u0432 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438.<\/li>\n<\/li>\n<\/ol>\n<p>   <strong>\u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435:<\/strong><br \/>\n   <a href=\"#1\">\u0412\u0432\u0435\u0434\u0435\u043d\u0438\u0435<\/a><br \/>\n   <a href=\"#2\">\u041a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u0438 2n-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b<\/a><br \/>\n   <a href=\"#3\">\u0424\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430<\/a><br \/>\n   <a href=\"#4\">\u0420\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u0438\u0435 \u043a \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u0431\u0438\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430<\/a><br \/>\n   <a href=\"#5\">\u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439<\/a>\n   <\/p>\n<p><\/center><\/p>\n<p><center><br \/>\n   <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ddTfUR7QBfY\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0412\u0432\u0435\u0434\u0435\u043d\u0438\u0435<\/h2>\n<p style=\"text-align: justify;\">\u041d\u0430\u0443\u0447\u0438\u0442\u044c\u0441\u044f \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u2014 \u044d\u0442\u043e \u043f\u0435\u0440\u0432\u044b\u0439 \u0448\u0430\u0433 \u043a \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044e \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u0434\u0440\u0443\u0433\u0438\u0445 \u043c\u0435\u0442\u043e\u0434\u043e\u0432 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u044d\u0442\u043e\u0442 \u043c\u0435\u0442\u043e\u0434 \u0438 \u0440\u0430\u0441\u0448\u0438\u0440\u0438\u043c \u0435\u0433\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u043d\u0430\u0441\u0442\u043e\u043b\u044c\u043a\u043e, \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u044d\u0442\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e. \u041f\u043e \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u0432\u044b \u043d\u0430\u0443\u0447\u0438\u0442\u0435\u0441\u044c \u043d\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d (\u0441\u0442\u0435\u043f\u0435\u043d\u0438 2), \u043d\u043e \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u044d\u0442\u0438 \u0436\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0434\u043b\u044f \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u043b\u044e\u0431\u044b\u0445 (2n)-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u041a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u0438 (2n)-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ddTfUR7QBfY&amp;t=96s\" target=\"_blank\" rel=\"noopener\"><strong>\u041a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u2014 \u044d\u0442\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u0432\u0442\u043e\u0440\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438.<\/strong><\/a> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2}+bx +c <\/span>\n<p style=\"text-align: justify;\">\u0441 <span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{R}<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span>. \u041e\u0434\u043d\u0430\u043a\u043e \u043d\u0430\u0448\u0435 \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u0435 \u043d\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0438\u0442\u0441\u044f \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0435\u0439 \u0442\u0430\u043a\u0438\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432; \u043c\u044b \u0442\u0430\u043a\u0436\u0435 \u043e\u0431\u0440\u0430\u0442\u0438\u043c \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043d\u0430 \u043e\u0431\u043e\u0431\u0449\u0451\u043d\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u2014 \u044d\u0442\u043e \u0432\u0441\u0435\u0433\u043e \u043b\u0438\u0448\u044c \u0447\u0430\u0441\u0442\u043d\u044b\u0439 \u0441\u043b\u0443\u0447\u0430\u0439. \u041c\u044b \u0433\u043e\u0432\u043e\u0440\u0438\u043c \u043e (2n)-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u043c \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0435, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0432\u043a\u043b\u044e\u0447\u0430\u0435\u0442 \u0432\u0441\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u0432\u0438\u0434\u0430<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2n}+bx^n +c <\/span>\n<p style=\"text-align: justify;\">\u0433\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{R}<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span>, \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">n\\in\\mathbb{N}<\/span>. \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0442\u0430\u043a\u0438\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432:<\/p>\n<ul style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 3x^2 -x + 1<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 7x^4 +5x^2 + 3<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">R(x) = -4x^6 +12x^3 + 2<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">S(x) = 21x^8 -75 x^4 -9<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u0438 \u0442\u0430\u043a \u0434\u0430\u043b\u0435\u0435.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u0424\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ddTfUR7QBfY&amp;t=193s\" target=\"_blank\" rel=\"noopener\"><strong>\u041a\u0430\u043a \u043c\u044b \u0443\u0436\u0435 \u0432\u0438\u0434\u0435\u043b\u0438, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u0438\u043c\u0435\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0432\u0438\u0434<\/strong><\/a><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2}+bx +c \\;\\; , \\;\\; a\\neq 0 <\/span>\n<p style=\"text-align: justify;\">\u0424\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u2014 \u044d\u0442\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0441\u043b\u043e\u0436\u043d\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0435\u0441\u043b\u0438 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u0430, \u0442\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta,\\gamma,\\delta \\in\\mathbb{R}<\/span>, \u0433\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha, \\gamma \\neq 0<\/span>, \u0442\u0430\u043a\u0438\u0435, \u0447\u0442\u043e:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^2 + bx + c <\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\">= (\\alpha x + \\beta)(\\gamma x + \\delta) <\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\">= \\alpha \\gamma \\left(x +\\displaystyle \\frac{\\beta}{\\alpha}\\right)\\left(x + \\frac{\\delta}{\\gamma}\\right) <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0422\u0430\u043a \u043a\u0430\u043a \u043b\u0435\u0432\u0430\u044f \u0438 \u043f\u0440\u0430\u0432\u0430\u044f \u0447\u0430\u0441\u0442\u0438 \u0440\u0430\u0432\u043d\u044b, \u043e\u0431\u0435 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0430\u043d\u043d\u0443\u043b\u0438\u0440\u0443\u044e\u0442\u0441\u044f, \u043a\u043e\u0433\u0434\u0430 \u043e\u0434\u043d\u0430 \u0438\u0437 \u043d\u0438\u0445 \u0430\u043d\u043d\u0443\u043b\u0438\u0440\u0443\u0435\u0442\u0441\u044f. \u041e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u043f\u0440\u0430\u0432\u0430\u044f \u0447\u0430\u0441\u0442\u044c \u0430\u043d\u043d\u0443\u043b\u0438\u0440\u0443\u0435\u0442\u0441\u044f, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x=-\\beta\/\\alpha<\/span> \u0438\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x=-\\delta\/\\gamma<\/span>. \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043f\u0440\u0438 \u043a\u0430\u043a\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \u043b\u0435\u0432\u0430\u044f \u0447\u0430\u0441\u0442\u044c \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0431\u0443\u0434\u0435\u0442 \u0430\u043d\u043d\u0443\u043b\u0438\u0440\u043e\u0432\u0430\u0442\u044c\u0441\u044f. \u0423 \u043d\u0430\u0441 \u0431\u0443\u0434\u0435\u0442:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\">ax^2 + bx + c<\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = 0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\">ax^2 + bx <\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = -c<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\">x^2 + \\displaystyle \\frac{b}{a}x <\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = - \\displaystyle \\frac{c}{a}<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right; background-color: #ffc0c0;\"><span class=\"katex-eq\" data-katex-display=\"false\">x^2 + \\displaystyle \\frac{b}{a}x + \\frac{b^2}{4a^2}<\/span><\/td>\n<td style=\"text-align: left; background-color: #ffc0c0;\"><span class=\"katex-eq\" data-katex-display=\"false\"> =\\displaystyle \\frac{b^2}{4a^2} -\\frac{c}{a} = \\frac{ab^2 - 4a^2 c}{4a^3} = \\frac{b^2 - 4ac }{4a^2}<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(x + \\displaystyle \\frac{b}{2a}\\right)^2<\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = \\displaystyle \\frac{b^2 - 4ac }{4a^2} <\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\"> x + \\displaystyle \\frac{b}{2a} <\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = \\pm \\sqrt{\\displaystyle \\frac{b^2 - 4ac }{4a^2}} = \\frac{\\pm\\sqrt{b^2 - 4ac }}{2a} <\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right; background-color: #a0ffa0;\"><span class=\"katex-eq\" data-katex-display=\"false\"> x <\/span><\/td>\n<td style=\"text-align: left; background-color: #a0ffa0;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = \\displaystyle \\frac{-b \\pm\\sqrt{b^2 - 4ac }}{2a} <\/span> \u2705<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0418\u0441\u0445\u043e\u0434\u044f \u0438\u0437 \u044d\u0442\u043e\u0433\u043e \u0440\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u044f, \u0443 \u043d\u0430\u0441 \u0431\u0443\u0434\u0443\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u044f \u0434\u043b\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438:<\/p>\n<ul style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha\\gamma = a<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\beta}{\\alpha} = - \\left(\\frac{-b + \\sqrt{b^2 - 4ac }}{2a} \\right)<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\delta}{\\gamma} = - \\left(\\frac{-b - \\sqrt{b^2 - 4ac }}{2a} \\right)<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0443 \u043d\u0430\u0441 \u043f\u043e\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u0435\u0445\u043d\u0438\u043a\u0430 \u0434\u043b\u044f \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u043b\u044e\u0431\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430 \u0432\u0442\u043e\u0440\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438. \u0415\u0441\u043b\u0438 \u0435\u0433\u043e \u043d\u0435\u043b\u044c\u0437\u044f \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u043e\u0432\u0430\u0442\u044c, \u044d\u0442\u043e \u0441\u0442\u0430\u043d\u0435\u0442 \u044f\u0441\u043d\u043e \u0438\u0437 \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442\u0430 (\u0435\u0441\u043b\u0438 \u043e\u043d \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u0435\u043d, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0432 \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u0447\u0438\u0441\u043b\u0430\u0445 \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u0430). \u0414\u043b\u044f \u0443\u0434\u043e\u0431\u0441\u0442\u0432\u0430 \u0432\u0432\u0435\u0434\u0451\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f:<\/p>\n<ul style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">x_1 =\\displaystyle \\frac{-b + \\sqrt{b^2 - 4ac }}{2a} <\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">x_2 =\\displaystyle \\frac{-b - \\sqrt{b^2 - 4ac }}{2a} <\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u0418 \u0432 \u0438\u0442\u043e\u0433\u0435 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0441\u0442\u0430\u0440\u0443\u044e, \u043d\u0430\u0434\u0451\u0436\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{x_{1,2} = \\displaystyle \\frac{-b \\pm \\sqrt{b^2 - 4ac }}{2a}}<\/span> \u2705<\/p>\n<p style=\"text-align: justify;\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430 \u043f\u0440\u0438\u043e\u0431\u0440\u0435\u0442\u0430\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{P(x) = ax^2 +bx + c = a(x-x_1)(x - x_2)}<\/span>\u2705<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u0420\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u0438\u0435 \u043a \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u0431\u0438\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ddTfUR7QBfY&amp;t=997s\" target=\"_blank\" rel=\"noopener\"><strong>\u042d\u0442\u043e\u0442 \u043c\u0435\u0442\u043e\u0434 \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u043b\u044f \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u0431\u0438\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430.<\/strong><\/a> \u041c\u0435\u0442\u043e\u0434 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = ax^4 + bx^2 + c = a(x^2)^2 + bx^2 + c = a (x^2 - x_1^2)(x^2-x_2^2) <\/span>\n<p style=\"text-align: justify;\">\u0413\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\"> x^2_{1,2} = \\displaystyle \\frac{-b \\pm \\sqrt{b^2 - 4ac }}{2a}<\/span>. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u043e\u0436\u043d\u043e \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c:<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = ax^4 + bx^2 + c = a\\left(x^2 - \\displaystyle \\frac{-b + \\sqrt{b^2 - 4ac }}{2a}\\right) \\left(x^2- \\frac{-b - \\sqrt{b^2 - 4ac }}{2a}\\right) <\/span>\n<p style=\"text-align: justify;\">\u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x_1^2<\/span> \u2014 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u043c\u043e\u0436\u043d\u043e \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u043c \u0441\u0443\u043c\u043c\u044b \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435. \u0415\u0441\u043b\u0438 \u043a\u043e\u0440\u043d\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u044b \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u044b\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u0430 \u0442\u043e\u043b\u044c\u043a\u043e \u0432 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u044b\u0445 \u0447\u0438\u0441\u043b\u0430\u0445.<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439:<\/h2>\n<p style=\"text-align: justify;\">\u0422\u0435\u043f\u0435\u0440\u044c \u0432\u0430\u0448\u0430 \u043e\u0447\u0435\u0440\u0435\u0434\u044c \u043e\u043f\u0440\u043e\u0431\u043e\u0432\u0430\u0442\u044c \u044d\u0442\u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u043d\u0430 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u0438\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u0445. \u042d\u0442\u0438 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u0431\u044b\u043b\u0438 \u0432\u044b\u0431\u0440\u0430\u043d\u044b \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u0441\u0442\u043e\u043b\u043a\u043d\u0443\u0442\u044c\u0441\u044f \u0441 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u043c\u0438 \u0442\u0440\u0443\u0434\u043d\u043e\u0441\u0442\u044f\u043c\u0438 \u0432 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438.<\/p>\n<h3>\u041f\u0435\u0440\u0432\u044b\u0439 \u0440\u0430\u0443\u043d\u0434<\/h3>\n<p style=\"text-align: justify;\">\u042d\u0442\u043e \u0442\u0435 \u0441\u0430\u043c\u044b\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u044f \u043f\u0440\u0438\u0432\u0451\u043b \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u043f\u043e\u0441\u0442\u0430:<\/p>\n<ol style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 3x^2 -x + 1<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 7x^4 +5x^2 + 3<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">R(x) = -4x^6 +12x^3 + 2<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">S(x) = 21x^8 -75 x^4 -9<\/span><\/li>\n<\/ol>\n<h3>\u0412\u0442\u043e\u0440\u043e\u0439 \u0440\u0430\u0443\u043d\u0434<\/h3>\n<p style=\"text-align: justify;\">\u0418 \u0432\u043e\u0442 \u0435\u0449\u0451 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0431\u043e\u043b\u0435\u0435 \u0441\u043b\u043e\u0436\u043d\u044b\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432:<\/p>\n<ol style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 78x^2 -21x - 13<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 27x^4 +5x^2 - 14<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">R(x) = 9x^6 +12x^3 - 16<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">S(x) = -9x^8 -2 x^4 + 10<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">T(x) = 5x^{12} -2 x^6 - 15<\/span><\/li>\n<\/ol>\n<h3>\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439<\/h3>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ilNTFyF7Hmo\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0424\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0438 2n-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430 \u0420\u0435\u0437\u044e\u043c\u0435: \u041d\u0430 \u044d\u0442\u043e\u043c \u0437\u0430\u043d\u044f\u0442\u0438\u0438 \u043c\u044b \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0438 2n-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 -\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 , \u0440\u0430\u0441\u043a\u043b\u0430\u0434\u044b\u0432\u0430\u044f \u0438\u0445 \u043d\u0430 \u043f\u0440\u043e\u0441\u0442\u044b\u0435 \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u0438. \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0431\u0443\u0434\u0443\u0442 \u043f\u0440\u043e\u0440\u0430\u0431\u043e\u0442\u0430\u043d\u044b \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u044b \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b. \u0426\u0435\u043b\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u041d\u0430\u0443\u0447\u0438\u0442\u044c\u0441\u044f \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u0432\u0438\u0434\u0430 . \u0412\u044b\u0432\u0435\u0441\u0442\u0438 \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043a\u043e\u0440\u043d\u0435\u0439. \u041f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u043c\u0435\u0442\u043e\u0434\u044b \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u043a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28831,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":4,"footnotes":""},"categories":[589,573],"tags":[],"class_list":["post-28841","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-589","category-573"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ 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