{"id":8557,"date":"2012-04-19T18:53:22","date_gmt":"2012-04-19T17:53:22","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8557"},"modified":"2022-01-06T19:20:44","modified_gmt":"2022-01-06T19:20:44","slug":"determina-o-binomio-discriminante","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8557","title":{"rendered":"Determina o bin\u00f3mio discriminante"},"content":{"rendered":"<p><ul id='GTTabs_ul_8557' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8557' class='GTTabs_curr'><a  id=\"8557_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8557' ><a  id=\"8557_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_8557'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Para cada uma das equa\u00e7\u00f5es determina o bin\u00f3mio discriminante e diz quantas solu\u00e7\u00f5es tem:<\/p>\n<ol>\n<li>${x^2} &#8211; 2x + 1 = 0$<\/li>\n<li>$2{x^2} &#8211; x &#8211; 1 = 0$<\/li>\n<li>${x^2} + 3x + 4 = 0$<\/li>\n<li>${a^2} &#8211; 7a &#8211; 18 = 0$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8557' onClick='GTTabs_show(1,8557)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8557'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><strong>N\u00famero de ra\u00edzes de uma equa\u00e7\u00e3o do 2.\u00ba grau<\/strong>: $$\\begin{array}{*{20}{c}} \u00a0 {a{x^2} + bx + c = 0}&amp; \\Leftrightarrow &amp;{x = \\frac{{ &#8211; b \\pm \\sqrt {{b^2} &#8211; 4ac} }}{{2a}}} \\end{array}$$ $$\\begin{array}{*{20}{c}} \u00a0 {{\\text{Bin\u00f3mio discriminante:}}}&amp;{}&amp;{\\Delta\u00a0 = {b^2} &#8211; 4ac} \\end{array}$$ $$\\begin{array}{*{20}{l}} \u00a0 {\\Delta\u00a0 &lt; 0}&amp; &#8211; &amp;{{\\text{A equa\u00e7\u00e3o n\u00e3o\u00a0tem ra\u00edzes reais }}} \\\\ \u00a0 {\\Delta\u00a0 = 0}&amp; &#8211; &amp;{{\\text{A equa\u00e7\u00e3o tem 1 raiz real}}} \\\\ \u00a0 {\\Delta\u00a0 &gt; 0}&amp; &#8211; &amp;{{\\text{A equa\u00e7\u00e3o tem 2 ra\u00edzes reais distintas}}} \\end{array}$$<\/p>\n<\/blockquote>\n<ol>\n<li>\u00a0 $${x^2} &#8211; 2x + 1 = 0$$ $$\\begin{array}{*{20}{l}} \u00a0 \\Delta &amp; = &amp;{{{( &#8211; 2)}^2} &#8211; 4 \\times 1 \\times 1} \\\\ \u00a0 {}&amp; = &amp;0 \\end{array}$$ Como $\\Delta\u00a0 = 0$, a equa\u00e7\u00e3o tem apenas uma solu\u00e7\u00e3o real.<br \/>\n\u00ad<\/li>\n<li>\u00a0 $$2{x^2} &#8211; x &#8211; 1 = 0$$ $$\\begin{array}{*{20}{l}} \u00a0 \\Delta &amp; = &amp;{{{( &#8211; 1)}^2} &#8211; 4 \\times 2 \\times ( &#8211; 1)} \\\\ \u00a0 {}&amp; = &amp;9 \\end{array}$$ Como $\\Delta\u00a0 &gt; 0$, a equa\u00e7\u00e3o tem duas solu\u00e7\u00f5es reais.<br \/>\n\u00ad<\/li>\n<li>\u00a0 $${x^2} + 3x + 4 = 0$$ $$\\begin{array}{*{20}{l}} \u00a0 \\Delta &amp; = &amp;{{3^2} &#8211; 4 \\times 1 \\times 4} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 7} \\end{array}$$ Como $\\Delta\u00a0 &lt; 0$, a equa\u00e7\u00e3o (\u00e9 imposs\u00edvel) n\u00e3o tem solu\u00e7\u00f5es reais.<br \/>\n\u00ad<\/li>\n<li>\u00a0 $${a^2} &#8211; 7a &#8211; 18 = 0$$ $$\\begin{array}{*{20}{l}} \u00a0 \\Delta &amp; = &amp;{{{( &#8211; 7)}^2} &#8211; 4 \\times 1 \\times ( &#8211; 18)} \\\\ \u00a0 {}&amp; = &amp;{121} \\end{array}$$ Como $\\Delta\u00a0 &gt; 0$, a equa\u00e7\u00e3o tem duas solu\u00e7\u00f5es reais.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8557' onClick='GTTabs_show(0,8557)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Para cada uma das equa\u00e7\u00f5es determina o bin\u00f3mio discriminante e diz quantas solu\u00e7\u00f5es tem: ${x^2} &#8211; 2x + 1 = 0$ $2{x^2} &#8211; x &#8211; 1 = 0$ ${x^2} + 3x&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19171,"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],"series":[],"class_list":["post-8557","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"],"views":4768,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat62.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8557","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=8557"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8557\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8557"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8557"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8557"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8557"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}