{"id":3378,"date":"2021-03-09T13:12:19","date_gmt":"2021-03-09T05:12:11","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=3378"},"modified":"2022-04-06T04:00:04","modified_gmt":"2022-04-05T20:00:04","slug":"quadratic_equation","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/quadratic_equation\/","title":{"rendered":"1. \u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"3378\" class=\"elementor elementor-3378\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b0bfce9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b0bfce9\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-45fa0d5\" data-id=\"45fa0d5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d9f1e98 elementor-widget elementor-widget-text-editor\" data-id=\"d9f1e98\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>1.0.0 \u54a9\u4fc2\u300c \u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b \u300d<\/h2><p>\u9996\u5148\u7b49\u6211\u5730\u4e00\u9f4a\u91cd\u6eab\u5413\u54a9\u4fc2\u300c\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u300d\u3002\u4ee5\u4e0b\u4fc2\u4e00\u689d\u300c\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u300d\u5605\u65b9\u7a0b\uff1a<\/p><p style=\"padding-left: 40px;\">\\(x^2+5x-7 = 0\\)<\/p><p>\u4f62\u53eb\u300c\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u300d\u4fc2\u56e0\u70ba:<\/p><ul><li>\u9019\u662f\u4e00\u689d<span style=\"color: #ff0000;\">\u65b9\u7a0b<\/span><\/li><li>\u7576\u4e2d\u53ea\u5f97<span style=\"color: #ff0000;\">\u4e00\u500b\u8b8a\u6578(\u5143)<\/span><\/li><li>\u5143\u5605<span style=\"color: #ff0000;\">\u6307\u6578 (\u5373\u6b21\u65b9)\u6700\u591a\u4fc22<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-75560e4 elementor-widget elementor-widget-text-editor\" data-id=\"75560e4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>1.0.1 \u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b \u7684\u4e00\u822c\u5f0f<\/h2><p>\u6211\u54cb\u901a\u5e38\u6703\u7528\u201c\u4e00\u822c\u5f0f\u201d\uff08general form\uff09\u569f\u8868\u793a\u4e00\u689d\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\uff1a<\/p><p style=\"padding-left: 40px;\">\\(ax^2 + bx + c = 0 \\quad \\quad\u00a0 (\u7576\u4e2da, b, c\u70ba\u6578\u5b57) \\)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2fd6300 elementor-widget elementor-widget-text-editor\" data-id=\"2fd6300\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>1.0.2 \u89e3 \u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b \u7684\u4e3b\u8981\u65b9\u6cd5 &#8211; \u7528\u8a08\u6578\u6a5f<\/h2><p>\u55ba\u4e2d\u5b78\u6587\u6191\u8ab2\u7a0b\u5165\u9762\uff0c\u8001\u5e2b\u61c9\u8a72\u6703\u6559\u5927\u5bb6\u4e0b\u9762\u5e7e\u500b\u65b9\u6cd5\u569f\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b(\u5373\u8a08\u500b\u7b54\u6848)\uff1a<\/p><ul><li>\u56e0\u5f0f\u5206\u89e3<\/li><li>\u914d\u65b9\u6cd5<\/li><li>\u5b8c\u5168\u5e73\u65b9<\/li><li>\u6c42\u6839\u516c\u5f0f<\/li><\/ul><p>\u4ee5\u4e0a\u5605\u65b9\u6cd5\u6703\u55ba\u5f8c\u9762\u5605\u7ae0\u7bc0\u6559\u5927\u5bb6\u3002<\/p><p>\u00a7 \u5c0d\u4e00\u822c\u540c\u5b78\u569f\u8b1b\uff08\u7279\u5225\u6578\u5b78\u4e0d\u597d\u7684\u540c\u5b78\uff09\uff0c\u6700\u7dca\u8981\u8b58\u5f97\u7528\u8a08\u7b97\u6a5f\u5165\u9762\u5605\u7a0b\u5f0f\u7be4\u5230\u500b\u7b54\u6848\u51fa\u569f\u3002<\/p><h3>1.0.2.1.\u00a0\u00a0\u00a0 \u4f7f\u7528\u8a08\u7b97\u6a5f\uff08Using the Calculator)<\/h3><p>\u9996\u5148\uff0c\u540c\u5b78\u8981\u78ba\u4fdd\u4f60\u90e8\u8a08\u7b97\u6a5f\u6709 \u201c\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u5605\u7a0b\u5f0f\u201d\u3002\u5187\u5605\u8a71\u53ef\u4ee5\u53bb\u00a0<a href=\"http:\/\/www.takwing.idv.hk\/studyroom\/ce_maths\/fx3650p-prog.htm\">http:\/\/www.takwing.idv.hk\/studyroom\/ce_maths\/fx3650p-prog.htm<\/a>\u00a0\uff0c\u55f0\u5ea6\u6709\u6559\u5927\u5bb6\u9ede\u5165\u500b\u7a0b\u5f0f\u3002<\/p><ul><li>\u4f46\u8acb\u6ce8\u610f\uff0c\u500b\u7a0b\u5f0f\u4fc2\u6bd4CASIO fx-3650p\u7528\u5605\uff0c\u5982\u679c\u4f60\u90e8\u6a5f\u4fc2\u5176\u4ed6\u578b\u865f\uff0c\u53ef\u4ee5\u81ea\u5df1\u4e0a\u7db2\u641c\u5c0b\u5413\u3002<\/li><\/ul><p>\u7528\u7a0b\u5f0f\u6642\u8981\u6ce8\u610f\u7684\u5e7e\u9ede\uff1a<\/p><ol><li>\u555f\u52d5\u7a0b\u5f0f\u5f8c<ul><li>\u6309\u6b21\u5e8f\u5165a, b, c\u4e09\u500b\u6578\u5b57(\u7528\u201cEXE\u201d\u4f5c\u70ba\u8f38\u5165\u9375)<\/li><li>\u5165\u5b8cc\uff0c\u8a08\u7b97\u6a5f\u6703\u99ac\u4e0a\u986f\u793a\u51fa\u5224\u5225\u5f0f\uff08b<sup>2<\/sup>\u00a0\u2013 4ac\uff09\u7684\u503c<\/li><li>\u6309\u201cEXE\u201d\u51fa\u7b2c\u4e00\u500b\u6839\uff08\u5373\u7b2c\u4e00\u500b\u7b54\u6848\uff09<\/li><li>\u518d\u6309\u201cEXE\u201d\u6703\u51fa\u7b2c\u4e8c\u500b\u6839\u3002<\/li><\/ul><\/li><li>\u4f7f\u7528\u7a0b\u5f0f\u6642\u5982\u6703\u51fa\u73fe\u201cMath ERROR\u201d\u3002\u4e3b\u8981\u539f\u56e0\u6709\u5169\u500b\uff1a<ul><li>\u4f60\u5165\u932f\u5497a, b, c\u4e09\u500b\u6578\uff01<br \/>\u5927\u5bb6\u8981\u7559\u610fax<sup>2<\/sup>\u00a0+ bx + c = 0\u4e2da,b,c\u5605\u6392\u4f4d\u540c\u6b63\u8ca0\u865f\uff01<\/li><li>\u689d\u65b9\u7a0b\u6839\u672c\u4fc2\u5187\u5f97\u89e3\u5605\uff01<br \/>\uff08\u201c\u5224\u5225\u5f0f &lt; 0\u201d\u6642\uff0c\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u4fc2\u5187\u5f97\u89e3\u5605\u3002\uff09<br \/>\u55ba\u4f9d\u500b\u60c5\u6cc1\uff0c\u984c\u76ee\u5605\u7b54\u6848\u53ef\u5beb\u6210\u201c\u56e0\u5224\u5225\u5f0f&lt;0\uff0c\u6240\u4ee5\u6c92\u6709\u5be6\u6839 (the equation has no real roots)\u201d\u3002<br \/>\u201c\u5be6\u6839\u201d\u4fc2\u6307&#8221;\u4fc2\u5be6\u6578\u5605\u6839\/\u7b54\u6848&#8221;\u3002<\/li><\/ul><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5b3c6b3 elementor-widget elementor-widget-accordion\" data-id=\"5b3c6b3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-9561\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-9561\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">\u7df4\u7fd2\uff1a   \u89e3    \\(3x^2 + 2x - 1 = 0\\)<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-9561\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-9561\"><p>\u7b54\u6848\uff1a\u00a0\u00a0\u00a0 \u00a0\u00a0<\/p><p style=\"padding-left: 40px;\">\\(\\begin{align}<br \/>&amp; 3x^2+2x-1 = 0 \\quad \\quad \\quad {\\color{Red} \\leftarrow \u8003\u8a66\u6642\u5514\u8a72\u6284\u4e00\u6b21\u984c\u76ee } \\\\<br \/>&amp; x = \\dfrac{1}{3}\u00a0 \\quad \u6216 \\quad x = -1 \\quad \\quad \\quad {\\color{Red} \\leftarrow \u7559\u610f\u8981\u7528\u201c\u6216\u201d\u5206\u958b\u5169\u500b\u7b54\u6848 } \\\\<br \/>\\end{align}\\)<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2320fa0 elementor-widget elementor-widget-text-editor\" data-id=\"2320fa0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul><li>\u5982\u679c\u8a08\u6578\u6a5f\u8a08\u5230\u5605\u4fc2\u9ede\u6578\uff0c\u540c\u5b78\u53ef\u4ee5\u8a66\u5413\u7528\u201c \u201d\u500b\u9375\u569f\u8f49\u8fd4\u505a\u5206\u6578\u3002<\/li><li>\u5982\u679c\u8a08\u7b97\u6a5f\u90fd\u8f49\u5514\u5230\uff0c\u53ef\u4ee5\u6284\u7b54\u6848\u81f3\u4e09\u4f4d\u6709\u4ea4\u6578\u5b57\uff08\u6216\u5c0f\u6578\u5f8c\u5169\u500b\u4f4d\uff09\u3002<\/li><li>\u500b\u4eba\u7d93\u9a57\uff1a\u5927\u90e8\u4efd\u984c\u76ee\u5605\u7b54\u6848\u90fd\u6703\u5e7e\u975a\u3002\u5982\u679c\u500b\u7b54\u6848\u597d\u602a\uff0c\u6700\u597dcheck\u5413\u6709\u5187\u7be4\u932f\u6a5f\u3002<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-ef3977e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ef3977e\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-f6ca5f0\" data-id=\"f6ca5f0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-7fd0d6a\" data-id=\"7fd0d6a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-f607c72\" data-id=\"f607c72\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f184de7 elementor-widget elementor-widget-text-editor\" data-id=\"f184de7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/quadratic_equation\/solve_by_factorization\/\">\u4ee5\u56e0\u5f0f\u6cd5\u89e3\u4e8c\u6b21\u65b9\u7a0b<\/a>\u00a0 <i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-e400c5b\" data-id=\"e400c5b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f2ff080 elementor-widget elementor-widget-sidebar\" data-id=\"f2ff080\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-5 > ul > li > a, .custom-menu-widget .ocean_custom_menu-5 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-5.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">DSE\u6578\u5b78 &#8211; \u5fc5\u4fee\u90e8\u5206\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-5 left dropdown-hover\"><ul id=\"menu-dsemaths_core\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1744\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1744\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/course-analysis\/\" class=\"menu-link\">\u8ab2\u7a0b\u5206\u6790 (Core)<\/a><\/li>\n<li  id=\"menu-item-1745\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children dropdown menu-item-1745\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/\" class=\"menu-link\">\u5514\u597d\u4ee5\u70ba\u5514\u99db\u8003 &#8211; \u76ee\u9304 <span class=\"nav-arrow fa fa-angle-down\"><\/span><\/a>\n<ul class=\"sub-menu\">\n\t<li  id=\"menu-item-4067\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4067\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/solving-equation\/\" class=\"menu-link\">1. \u89e3\u65b9\u7a0b<\/a><\/li>\n\t<li  id=\"menu-item-4068\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4068\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/polynomials\/\" class=\"menu-link\">2. \u591a\u9805\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4069\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4069\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/laws-of-indices\/\" class=\"menu-link\">3. \u6307\u6578\u5b9a\u5f8b<\/a><\/li>\n\t<li  id=\"menu-item-4070\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4070\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/factorization\/\" class=\"menu-link\">4. \u56e0\u5f0f\u5206\u89e3<\/a><\/li>\n\t<li  id=\"menu-item-4071\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4071\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/formulae\/\" class=\"menu-link\">5. \u516c\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4072\" class=\"menu-item 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