{"id":14462,"date":"2018-04-13T23:35:07","date_gmt":"2018-04-13T22:35:07","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14462"},"modified":"2022-01-07T21:32:03","modified_gmt":"2022-01-07T21:32:03","slug":"considera-a-seguinte-equacao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14462","title":{"rendered":"Considera a seguinte equa\u00e7\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_14462' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14462' class='GTTabs_curr'><a  id=\"14462_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14462' ><a  id=\"14462_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_14462'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera a seguinte equa\u00e7\u00e3o:<\/p>\n<p>\\[2{x^2} + 5x &#8211; 3 = 0\\]<\/p>\n<ol>\n<li>Identifica os coeficientes de cada termo da equa\u00e7\u00e3o.<\/li>\n<li>Calcula o valor do bin\u00f3mio discriminante.<\/li>\n<li>A partir da al\u00ednea anterior, o que podemos concluir quanto ao n\u00famero de solu\u00e7\u00f5es da equa\u00e7\u00e3o?<\/li>\n<li>Resolve a equa\u00e7\u00e3o, sem recorreres \u00e0 f\u00f3rmula resolvente.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14462' onClick='GTTabs_show(1,14462)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14462'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Considera a seguinte equa\u00e7\u00e3o:<\/p>\n<p>\\[2{x^2} + 5x &#8211; 3 = 0\\]<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<ol>\n<li>Os coeficientes de cada termo da equa\u00e7\u00e3o s\u00e3o: \\(a = 2\\), \\(b = 5\\) e \\(c = &#8211; 3\\).<br \/>\u00ad<\/li>\n<li>O valor do bin\u00f3mio discriminante \u00e9 49:<br \/>\\(\\Delta = {5^2} &#8211; 4 \\times 2 \\times \\left( { &#8211; 3} \\right) = 25 + 24 = 49\\).<br \/>\u00ad<\/li>\n<li>A equa\u00e7\u00e3o tem duas solu\u00e7\u00f5es, pois o bin\u00f3mio discriminante \u00e9 positivo.<br \/>\u00ad<\/li>\n<li>Ora,<br \/>\\[\\begin{array}{*{20}{l}}{2{x^2} + 5x &#8211; 3 = 0}&amp; \\Leftrightarrow &amp;{{x^2} + \\frac{5}{2}x &#8211; \\frac{3}{2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{{{\\left( {x &#8211; \\frac{5}{4}} \\right)}^2} &#8211; \\frac{{25}}{{16}} &#8211; \\frac{3}{2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{{{\\left( {x &#8211; \\frac{5}{4}} \\right)}^2} = \\frac{{49}}{{16}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x &#8211; \\frac{5}{4} = &#8211; \\frac{7}{4}}&amp; \\vee &amp;{x &#8211; \\frac{5}{4} = \\frac{7}{4}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; \\frac{1}{2}}&amp; \\vee &amp;{x = 3}\\end{array}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left\\{ { &#8211; \\frac{1}{2},\\;3} \\right\\}}\\end{array}\\]<\/li>\n<\/ol>\n\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14462' onClick='GTTabs_show(0,14462)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a seguinte equa\u00e7\u00e3o: \\[2{x^2} + 5x &#8211; 3 = 0\\] Identifica os coeficientes de cada termo da equa\u00e7\u00e3o. Calcula o valor do bin\u00f3mio discriminante. A partir da al\u00ednea anterior, o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14057,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,305,495,306],"series":[],"class_list":["post-14462","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-binomio-discriminante","tag-completamento-do","tag-equacao-do-2-o-grau"],"views":2955,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat02.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14462","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=14462"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14462\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14057"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14462"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14462"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14462"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14462"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}