{"id":3612,"date":"2025-04-11T00:32:46","date_gmt":"2025-04-10T21:32:46","guid":{"rendered":"https:\/\/currconv.ru\/blog\/?p=3612"},"modified":"2025-05-03T15:28:27","modified_gmt":"2025-05-03T12:28:27","slug":"kvadratnoe_uravneniy","status":"publish","type":"post","link":"https:\/\/currconv.ru\/blog\/kvadratnoe_uravneniy\/","title":{"rendered":"\u041a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439. \u0414\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442. \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442\u0430. \u041f\u0440\u0438\u043c\u0435\u0440\u044b."},"content":{"rendered":"<div class=\"entry-content\" itemprop=\"text\">\n<div class=\"fpm_start\"><\/div>\n<p><strong>\u041a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> &#8211; \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432\u0438\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">ax^2+bx+c=0<\/span>, \u0433\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> &#8211; \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, <span class=\"katex-eq\" data-katex-display=\"false\">c<\/span> &#8211; \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u044b\u0439 \u0447\u043b\u0435\u043d,  \u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> &#8211; \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/currconv.ru\/blog\/wp-content\/uploads\/2025\/04\/maxresdefault.jpg\" alt=\"\" width=\"1280\" height=\"720\" class=\"aligncenter size-full wp-image-3616\" srcset=\"https:\/\/currconv.ru\/blog\/wp-content\/uploads\/2025\/04\/maxresdefault.jpg 1280w, https:\/\/currconv.ru\/blog\/wp-content\/uploads\/2025\/04\/maxresdefault-300x169.jpg 300w, https:\/\/currconv.ru\/blog\/wp-content\/uploads\/2025\/04\/maxresdefault-1024x576.jpg 1024w, https:\/\/currconv.ru\/blog\/wp-content\/uploads\/2025\/04\/maxresdefault-768x432.jpg 768w\" sizes=\"auto, (max-width: 1280px) 100vw, 1280px\" \/><\/p>\n<p>\u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0432\u0438\u0434\u043e\u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/p>\n<ol class=\"wp-block-list\">\n<li><strong>\u041f\u043e\u043b\u043d\u043e\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> &#8211; \u044d\u0442\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c <span class=\"katex-eq\" data-katex-display=\"false\">a\\neq0<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">b\\neq0<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">c\\neq0<\/span>.<\/li>\n<li><strong>\u041d\u0435\u043f\u043e\u043b\u043d\u043e\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> &#8211; \u044d\u0442\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c <span class=\"katex-eq\" data-katex-display=\"false\">b=0<\/span> \u0438\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">c=0<\/span>.<\/li>\n<li><strong>\u041f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> &#8211; \u044d\u0442\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 <span class=\"katex-eq\" data-katex-display=\"false\">a=1<\/span> (\u0435\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">a\\neq1<\/span>, \u0442\u043e\u0433\u0434\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u043d\u0435\u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u043c<\/strong>).<\/li>\n<\/ol>\n<p>\u0421\u0430\u043c\u044b\u0439 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043a\u043e\u0440\u043d\u0435\u0439 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f &#8211; \u0447\u0435\u0440\u0435\u0437 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 <strong>\u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442\u0430<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">D<\/span>. \u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439:<\/p>\n<ol class=\"wp-block-list\">\n<li>\u041f\u0440\u0438\u0432\u043e\u0434\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043a \u0432\u0438\u0434\u0443 <span class=\"katex-eq\" data-katex-display=\"false\">ax^2+bx+c=0<\/span><\/li>\n<li>\u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">D=b^2-4ac<\/span>.<br \/><span class=\"katex-eq\" data-katex-display=\"false\">\\bullet<\/span> \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">D&gt;0<\/span>, \u0442\u043e\u0433\u0434\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438\u043c\u0435\u0435\u0442 \u0434\u0432\u0430 \u043a\u043e\u0440\u043d\u044f.<br \/><span class=\"katex-eq\" data-katex-display=\"false\">\\bullet<\/span> \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">D=0<\/span>, \u0442\u043e\u0433\u0434\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438\u043c\u0435\u0435\u0442 \u043e\u0434\u0438\u043d \u043a\u043e\u0440\u043d\u044f.<br \/><span class=\"katex-eq\" data-katex-display=\"false\">\\bullet<\/span> \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">D&lt;0<\/span>, \u0442\u043e\u0433\u0434\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u043a\u043e\u0440\u043d\u0435\u0439.<\/li>\n<li>\u041d\u0430\u0445\u043e\u0434\u0438\u043c \u043a\u043e\u0440\u043d\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 <span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle x=\\frac{-b \\pm \\sqrt{D}}{2a}<\/span>. <br \/>\u041e\u0442\u0441\u044e\u0434\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:  <span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\begin{cases} {x_1=\\frac{-b + \\sqrt{D}}{2a}} \\\\ {x_2=\\frac{-b &#8212; \\sqrt{D}}{2a}} \\end{cases}<\/span>.<\/li>\n<\/ol>\n<hr class=\"wp-block-separator\"\/>\n<p>\u0420\u0435\u0448\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432:<\/p>\n<p><strong>\u041f\u0440\u0438\u043c\u0435\u0440 1:<\/strong><\/p>\n<p><span class=\"katex-eq\" data-katex-display=\"true\">x^2+2x+3=0<\/span><br \/><span class=\"katex-eq\" data-katex-display=\"false\">D=b^2-4ac=2^2-4 \\cdot 1 \\cdot 3=-8<\/span> &#8211; \u0440\u0435\u0448\u0435\u043d\u0438\u0439 \u043d\u0435\u0442, \u0442. \u043a. <span class=\"katex-eq\" data-katex-display=\"false\">D&lt;0<\/span>.<\/p>\n<p><strong>\u041f\u0440\u0438\u043c\u0435\u0440 2:<\/strong><\/p>\n<p><span class=\"katex-eq\" data-katex-display=\"true\">2x^2+5x+2=0<\/span><br \/><span class=\"katex-eq\" data-katex-display=\"false\">D=b^2-4ac=5^2-4 \\cdot 2 \\cdot 2=9<\/span> &#8211; \u0434\u0432\u0430 \u043a\u043e\u0440\u043d\u044f, \u0442. \u043a. <span class=\"katex-eq\" data-katex-display=\"false\">D&gt;0<\/span>.<br \/><span class=\"katex-eq\" data-katex-display=\"false\">x_1=\\frac{-b + \\sqrt{D}}{2a}=\\frac{-5+\\sqrt9}{2\\cdot2}=-0,5<\/span><br \/><span class=\"katex-eq\" data-katex-display=\"false\">x_2=\\frac{-b + \\sqrt{D}}{2a}=\\frac{-5-\\sqrt9}{2\\cdot2}=-2<\/span><\/p>\n<\/p>\n<p><script data-noptimize=\"\" data-wpfc-render=\"false\">\nfpm_start( \"true\" );\n<\/script><\/p>\n<p><strong>\u041f\u0440\u0438\u043c\u0435\u0440 3:<\/strong><\/p>\n<p><span class=\"katex-eq\" data-katex-display=\"true\">4x^2+4x+1=0<\/span><br \/><span class=\"katex-eq\" data-katex-display=\"false\">D=b^2-4ac=4^2-4 \\cdot 4 \\cdot 1=0<\/span> &#8211; \u043e\u0434\u0438\u043d \u043a\u043e\u0440\u043d\u044f, \u0442. \u043a. <span class=\"katex-eq\" data-katex-display=\"false\">D=0<\/span>.<br \/><span class=\"katex-eq\" data-katex-display=\"false\">x_1=\\frac{-b + \\sqrt{D}}{2a}=\\frac{-4+\\sqrt0}{2\\cdot4}=-0,5<\/span><br \/><span class=\"katex-eq\" data-katex-display=\"false\">x_2=\\frac{-b + \\sqrt{D}}{2a}=\\frac{-4-\\sqrt0}{2\\cdot2}=-0,5<\/span><\/p>\n<p>\u041a\u0430\u043a \u0432\u0438\u0434\u0438\u043c, \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u043e\u0441\u044c \u043e\u0434\u0438\u043d \u043a\u043e\u0440\u0435\u043d\u044c, \u0442. \u043a. \u043a\u043e\u0440\u0435\u043d\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u0438\u0437 \u043d\u0443\u043b\u044f \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e. \u041f\u043e\u044d\u0442\u043e\u043c\u0443, \u0435\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">D=0<\/span>, \u0442\u043e\u0433\u0434\u0430 \u043a\u043e\u0440\u0435\u043d\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle x=\\frac{-b}{2a}<\/span>.<\/p>\n<div class=\"fpm_end\"><\/div>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u041a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 &#8211; \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432\u0438\u0434\u0430 ax^2+bx+c=0, \u0433\u0434\u0435 a, b &#8211; \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, c &#8211; \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u044b\u0439 \u0447\u043b\u0435\u043d, \u0430 x &#8211; \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f. \u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0432\u0438\u0434\u043e\u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435: \u041f\u043e\u043b\u043d\u043e\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 &#8211; \u044d\u0442\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c a\\neq0, b\\neq0 \u0438 c\\neq0. \u041d\u0435\u043f\u043e\u043b\u043d\u043e\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 &#8211; \u044d\u0442\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c b=0 \u0438\u043b\u0438 c=0. \u041f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3615,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3612","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-1"],"_links":{"self":[{"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/posts\/3612","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/comments?post=3612"}],"version-history":[{"count":3,"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/posts\/3612\/revisions"}],"predecessor-version":[{"id":3617,"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/posts\/3612\/revisions\/3617"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/media\/3615"}],"wp:attachment":[{"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/media?parent=3612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/categories?post=3612"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/currconv.ru\/blog\/wp-json\/wp\/v2\/tags?post=3612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}