{"id":14398,"date":"2018-04-12T16:29:14","date_gmt":"2018-04-12T15:29:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14398"},"modified":"2022-01-06T23:15:11","modified_gmt":"2022-01-06T23:15:11","slug":"considera-as-equacoes-do-2-o-grau","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14398","title":{"rendered":"Considera as equa\u00e7\u00f5es do 2.\u00ba grau"},"content":{"rendered":"<p><ul id='GTTabs_ul_14398' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14398' class='GTTabs_curr'><a  id=\"14398_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14398' ><a  id=\"14398_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_14398'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera as seguintes equa\u00e7\u00f5es do 2.\u00ba grau.<\/p>\n<table class=\" aligncenter\">\n<tbody>\n<tr>\n<td style=\"width: 148.96px;\">\\({x^2} + 4x &#8211; 12 = 0\\)<\/td>\n<td style=\"width: 144.95px;\">\\( &#8211; 2{x^2} = 0\\)<\/td>\n<td style=\"width: 140.96px;\">\\({x^2} &#8211; 25 = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 148.96px;\">\\( &#8211; 8{x^2} + 6x = 0\\)<\/td>\n<td style=\"width: 144.95px;\">\\(9{x^2} &#8211; 6x &#8211; 2 = 0\\)<\/td>\n<td style=\"width: 140.96px;\">\\({x^2} &#8211; 8x + 7 = 0\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>Identifica as equa\u00e7\u00f5es do 2.\u00ba grau completas e as equa\u00e7\u00f5es do 2.\u00ba grau incompletas.<\/li>\n<li>Copia e completa uma tabela como a seguinte.<br \/>\n<table class=\" aligncenter\">\n<tbody>\n<tr>\n<td><strong>Equa\u00e7\u00e3o<\/strong><\/td>\n<td><strong>Coeficiente de\u00a0\\({x^2}\\)<br \/>\n(a)<\/strong><\/td>\n<td><strong>Coeficiente de\u00a0\\(x\\)<br \/>\n(b)<\/strong><\/td>\n<td><strong>Termo independente<br \/>\n(c)<\/strong><\/td>\n<\/tr>\n<tr>\n<td>\\({x^2} + 4x &#8211; 12 = 0\\)<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\( &#8211; 2{x^2} = 0\\)<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\({x^2} &#8211; 25 = 0\\)<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\( &#8211; 8{x^2} + 6x = 0\\)<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(9{x^2} &#8211; 6x &#8211; 2 = 0\\)<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\({x^2} &#8211; 8x + 7 = 0\\)<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Resolve cada uma das equa\u00e7\u00f5es do 2.\u00ba grau, usando, quando necess\u00e1rio, a f\u00f3rmula resolvente.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14398' onClick='GTTabs_show(1,14398)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14398'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table class=\" aligncenter\">\n<tbody>\n<tr>\n<td style=\"width: 148.96px;\">Equa\u00e7\u00f5es do 2.\u00ba grau completas:<\/td>\n<td style=\"width: 148.96px;\">\\({x^2} + 4x &#8211; 12 = 0\\)<\/td>\n<td style=\"width: 144.95px;\"><span style=\"font-family: Verdana;\">\\(9{x^2} &#8211; 6x &#8211; 2 = 0\\)\u00a0<\/span><\/td>\n<td style=\"width: 140.06px;\"><span style=\"font-family: Verdana;\">\\({x^2} &#8211; 8x + 7 = 0\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 148.96px;\">Equa\u00e7\u00f5es do 2.\u00ba grau incompletas:<\/td>\n<td style=\"width: 148.96px;\">\\( &#8211; 8{x^2} + 6x = 0\\)<\/td>\n<td style=\"width: 144.95px;\"><span style=\"font-family: Verdana;\">\\( &#8211; 2{x^2} = 0\\)\u00a0<\/span><\/td>\n<td style=\"width: 140.06px;\">\\({x^2} &#8211; 25 = 0\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>\u00a0A indica\u00e7\u00e3o das equa\u00e7\u00f5es completas e incompletas est\u00e1 feita acima.<br \/>\n\u00ad<br \/>\n<b><\/b><i><\/i><u><\/u><\/li>\n<li>Copia e completa uma tabela como a seguinte.<br \/>\n\u00ad<\/p>\n<table class=\" aligncenter\">\n<tbody>\n<tr>\n<td><strong>Equa\u00e7\u00e3o<\/strong><\/td>\n<td><strong>Coeficiente de\u00a0\\({x^2}\\)<br \/>\n(a)<\/strong><\/td>\n<td><strong>Coeficiente de\u00a0\\(x\\)<br \/>\n(b)<\/strong><\/td>\n<td><strong>Termo independente<br \/>\n(c)<\/strong><\/td>\n<\/tr>\n<tr>\n<td>\\({x^2} + 4x &#8211; 12 = 0\\)<\/td>\n<td><span style=\"color: #0000ff;\">\u00a01<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a04<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a0-12<\/span><\/td>\n<\/tr>\n<tr>\n<td>\\( &#8211; 2{x^2} = 0\\)<\/td>\n<td><span style=\"color: #0000ff;\">\u00a0-2<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a00<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a00<\/span><\/td>\n<\/tr>\n<tr>\n<td>\\({x^2} &#8211; 25 = 0\\)<\/td>\n<td><span style=\"color: #0000ff;\">\u00a01<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a00<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a0-25<\/span><\/td>\n<\/tr>\n<tr>\n<td>\\( &#8211; 8{x^2} + 6x = 0\\)<\/td>\n<td><span style=\"color: #0000ff;\">\u00a0-8<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a06<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a00<\/span><\/td>\n<\/tr>\n<tr>\n<td>\\(9{x^2} &#8211; 6x &#8211; 2 = 0\\)<\/td>\n<td><span style=\"color: #0000ff;\">\u00a09<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a0-6<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a0-2<\/span><\/td>\n<\/tr>\n<tr>\n<td>\\({x^2} &#8211; 8x + 7 = 0\\)<\/td>\n<td><span style=\"color: #0000ff;\">\u00a01<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a0-8<\/span><\/td>\n<td><span style=\"color: #0000ff;\">\u00a07<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00ad<\/li>\n<li>Resolve cada uma das equa\u00e7\u00f5es do 2.\u00ba grau, usando, quando necess\u00e1rio, a f\u00f3rmula resolvente.<br \/>\n\u00ad<\/li>\n<\/ol>\n<blockquote>\n<p><strong>F\u00f3rmula resolvente da equa\u00e7\u00e3o do 2.\u00ba grau<\/strong>:<\/p>\n<p>$$\\begin{array}{*{20}{c}}<br \/>\n{a{x^2} + bx + c = 0}&amp; \\Leftrightarrow &amp;{x = \\frac{{ &#8211; b \\pm \\sqrt {{b^2} &#8211; 4ac} }}{{2a}}}&amp;{(a \\ne 0)}<br \/>\n\\end{array}$$<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{x^2} + 4x &#8211; 12 = 0}&amp; \\Leftrightarrow &amp;{x = \\frac{{ &#8211; 4 \\mp \\sqrt {{4^2} &#8211; 4 \\times 1 \\times \\left( { &#8211; 12} \\right)} }}{{2 \\times 1}}}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{ &#8211; 4 \\mp \\sqrt {64} }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{ &#8211; 4 &#8211; 8}}{2}}&amp; \\vee &amp;{x = \\frac{{ &#8211; 4 + 8}}{2}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 6}&amp; \\vee &amp;{x = 2}\\end{array}}\\end{array}\\]<\/p>\n<p>\u00ad<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{ &#8211; 2{x^2} = 0}&amp; \\Leftrightarrow &amp;{{x^2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x = 0}\\end{array}\\]<\/p>\n<p>\u00ad<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{x^2} &#8211; 25 = 0}&amp; \\Leftrightarrow &amp;{{x^2} = 25}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 5}&amp; \\vee &amp;{x = 5}\\end{array}}\\end{array}\\]<\/p>\n<p>\u00ad<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{ &#8211; 8{x^2} + 6x = 0}&amp; \\Leftrightarrow &amp;{2x\\left( { &#8211; 4x + 3} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{2x = 0}&amp; \\vee &amp;{ &#8211; 4x + 3 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x = \\frac{3}{4}}\\end{array}}\\end{array}\\]<\/p>\n<p>\u00ad<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{9{x^2} &#8211; 6x &#8211; 2 = 0}&amp; \\Leftrightarrow &amp;{x = \\frac{{6 \\mp \\sqrt {{{\\left( { &#8211; 6} \\right)}^2} &#8211; 4 \\times 9 \\times \\left( { &#8211; 2} \\right)} }}{{2 \\times 9}}}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{6 \\mp \\sqrt {108} }}{{18}}}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{6 \\mp 6\\sqrt 3 }}{{18}}}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{1 \\mp \\sqrt 3 }}{3}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{1 &#8211; \\sqrt 3 }}{3}}&amp; \\vee &amp;{x = \\frac{{1 + \\sqrt 3 }}{3}}\\end{array}}\\end{array}\\]<\/p>\n<p>\u00ad<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{x^2} &#8211; 8x + 7 = 0}&amp; \\Leftrightarrow &amp;{x = \\frac{{8 \\mp \\sqrt {{{\\left( { &#8211; 8} \\right)}^2} &#8211; 4 \\times 1 \\times 7} }}{{2 \\times 1}}}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{8 \\mp \\sqrt {36} }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{8 &#8211; 6}}{2}}&amp; \\vee &amp;{x = \\frac{{8 + 6}}{2}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 1}&amp; \\vee &amp;{x = 7}\\end{array}}\\end{array}\\]<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14398' onClick='GTTabs_show(0,14398)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera as seguintes equa\u00e7\u00f5es do 2.\u00ba grau. \\({x^2} + 4x &#8211; 12 = 0\\) \\( &#8211; 2{x^2} = 0\\) \\({x^2} &#8211; 25 = 0\\) \\( &#8211; 8{x^2} + 6x = 0\\)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14095,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,196,306,304],"series":[],"class_list":["post-14398","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-equacoes-do-2-o-grau","tag-9-o-ano","tag-casos-notaveis","tag-equacao-do-2-o-grau","tag-formula-resolvente"],"views":990,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat40.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14398","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14398"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14398\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14095"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14398"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}