{"id":14418,"date":"2018-04-12T18:45:06","date_gmt":"2018-04-12T17:45:06","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14418"},"modified":"2022-01-06T23:22:11","modified_gmt":"2022-01-06T23:22:11","slug":"sobre-uma-equacao-do-2-o-grau","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14418","title":{"rendered":"Sobre uma equa\u00e7\u00e3o do 2.\u00ba grau"},"content":{"rendered":"<p><ul id='GTTabs_ul_14418' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14418' class='GTTabs_curr'><a  id=\"14418_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14418' ><a  id=\"14418_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_14418'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Para que valores do par\u00e2metro\u00a0\u03b1 a equa\u00e7\u00e3o do segundo grau\u00a0\\[{x^2} + x + \\alpha = 0\\] possui duas solu\u00e7\u00f5es?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14418' onClick='GTTabs_show(1,14418)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14418'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Para que a equa\u00e7\u00e3o\u00a0\\({x^2} + x + \\alpha = 0\\) possua duas solu\u00e7\u00f5es, o seu bin\u00f3mio discriminante tem de ser positivo.<\/p>\n<p>Assim, temos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\Delta &gt; 0}&amp; \\Leftrightarrow &amp;{{1^2} &#8211; 4 \\times 1 \\times \\alpha &gt; 0}\\\\{}&amp; \\Leftrightarrow &amp;{1 &#8211; 4\\alpha &gt; 0}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 4\\alpha &gt; &#8211; 1}\\\\{}&amp; \\Leftrightarrow &amp;{\\alpha &lt; \\frac{1}{4}}\\\\{}&amp; \\Leftrightarrow &amp;{\\alpha \\in \\left] { &#8211; \\infty ,\\;\\frac{1}{4}} \\right[}\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14418' onClick='GTTabs_show(0,14418)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Para que valores do par\u00e2metro\u00a0\u03b1 a equa\u00e7\u00e3o do segundo grau\u00a0\\[{x^2} + x + \\alpha = 0\\] possui duas solu\u00e7\u00f5es? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/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":[426,305,306,304],"series":[],"class_list":["post-14418","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-equacao-do-2-o-grau","tag-formula-resolvente"],"views":2528,"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\/14418","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=14418"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14418\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14418"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14418"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14418"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}