{"id":232,"date":"2026-10-03T18:20:00","date_gmt":"2026-10-03T17:20:00","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/equacao-cubica\/"},"modified":"2026-10-03T18:20:00","modified_gmt":"2026-10-03T17:20:00","slug":"equacao-cubica-2","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/matematica\/equacao-cubica-2\/","title":{"rendered":"Resolvedor de Equa\u00e7\u00f5es C\u00fabicas"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Equa\u00e7\u00e3o C\u00fabica<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"232\" data-favorite-title=\"Equa\u00e7\u00e3o C\u00fabica\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/matematica\/equacao-cubica-2\/\" data-favorite-excerpt=\"Resolve qualquer equa\u00e7\u00e3o c\u00fabica ax\u00b3 + bx\u00b2 + cx + d = 0 pelo m\u00e9todo de Cardano. Introduza os quatro coeficientes e a calculadora devolve as ra\u00edzes reais, assinala as complexas e deteta ra\u00edzes repetidas.\" aria-label=\"Adicionar aos favoritos\" data-favorite-icon=\"icon icon-algebra\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/pt\/matematica\/equacao-cubica-2\/\" method=\"POST\" class=\"calculator\" id=\"calculator-232\" data-post=\"232\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Campos de entrada<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Coeficiente a<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"coeficiente_a\" id=\"field-1\" step=\"any\" value=\"1\"\/><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Coeficiente b<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"coeficiente_b\" id=\"field-2\" step=\"any\" value=\"8\"\/><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Coeficiente c<\/label><div class=\"term\">c<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"coeficiente_c\" id=\"field-3\" step=\"any\" value=\"16\"\/><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Coeficiente d<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"coeficiente_d\" id=\"field-4\" step=\"any\" value=\"0\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalcular\" id=\"calculate-button\" data-post=\"232\">Calcular<\/button><button type=\"reset\">Redefinir<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calcular automaticamente<\/label><small>Se ativado, o resultado \u00e9 atualizado automaticamente quando voc\u00ea altera qualquer valor.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Seus resultados<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Raiz x\u2081<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Raiz x\u2082<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Raiz x\u2083<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copiar link para este c\u00e1lculo<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Deixar um coment\u00e1rio<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"232\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">O que voc\u00ea achou deste resultado?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Curti <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">\u00datil <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confuso <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Decepcionado <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Impreciso <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>F\u00f3rmula da Equa\u00e7\u00e3o C\u00fabica<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">F\u00f3rmula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ ax^3 + bx^2 + cx + d = 0, \\quad a \\neq 0 \\]\n\\[ \\text{Substitua } x = t - \\frac{b}{3a} \\text{ para obter a c\u00fabica reduzida: } t^3 + pt + q = 0 \\]\n\\[ p = \\frac{3ac - b^2}{3a^2}, \\qquad q = \\frac{2b^3 - 9abc + 27a^2 d}{27a^3} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Onde:<\/strong><\/p>\n<ul>\n<li>\\(a, b, c, d\\) \u2014 os coeficientes da equa\u00e7\u00e3o c\u00fabica<\/li>\n<li>\\(p, q\\) \u2014 os coeficientes da c\u00fabica reduzida ap\u00f3s eliminar o termo quadr\u00e1tico<\/li>\n<\/ul>\n<p>A partir daqui, aplica-se o m\u00e9todo de Cardano. A grandeza-chave \u00e9 o discriminante \\(\\Delta = \\left(\\frac{q}{2}\\right)^2 + \\left(\\frac{p}{3}\\right)^3\\):<\/p>\n<ul>\n<li>Se \\(\\Delta &gt; 0\\), existe uma raiz real, dada por<br \/>\\( t = \\sqrt[3]{-\\frac{q}{2} + \\sqrt{\\Delta}} + \\sqrt[3]{-\\frac{q}{2} - \\sqrt{\\Delta}} \\)<\/li>\n<li>Se \\(\\Delta = 0\\), todas as ra\u00edzes s\u00e3o reais e pelo menos duas coincidem: \\( t_1 = 2\\sqrt[3]{-\\frac{q}{2}} \\), \\( t_2 = t_3 = -\\sqrt[3]{-\\frac{q}{2}} \\)<\/li>\n<li>Se \\(\\Delta &lt; 0\\), h\u00e1 tr\u00eas ra\u00edzes reais distintas, obtidas com a forma trigonom\u00e9trica \\( t_k = 2\\sqrt{-\\frac{p}{3}} \\cos\\left(\\frac{\\theta + 2\\pi k}{3}\\right) \\), onde \\( \\cos\\theta = \\frac{3q}{2p}\\sqrt{-\\frac{3}{p}} \\), \\( k = 0, 1, 2 \\)<\/li>\n<\/ul>\n<p>Cada raiz da equa\u00e7\u00e3o original \u00e9 recuperada por retro-substitui\u00e7\u00e3o: \\( x = t - \\frac{b}{3a} \\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Equa\u00e7\u00e3o C\u00fabica \u2013 Exemplo de C\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> resolver \\( x^3 + 8x^2 + 16x = 0 \\) (coeficientes \\( a = 1 \\), \\( b = 8 \\), \\( c = 16 \\), \\( d = 0 \\) \u2014 os valores predefinidos da calculadora).<\/p>\n<p>\\[ p = \\frac{3 \\cdot 1 \\cdot 16 - 8^2}{3 \\cdot 1^2} = \\frac{48 - 64}{3} = -\\frac{16}{3}, \\qquad q = \\frac{2 \\cdot 8^3 - 9 \\cdot 1 \\cdot 8 \\cdot 16 + 27 \\cdot 1^2 \\cdot 0}{27 \\cdot 1^3} = \\frac{64}{27} \\]<\/p>\n<p>\\[ \\Delta = \\left(\\frac{q}{2}\\right)^2 + \\left(\\frac{p}{3}\\right)^3 = \\left(\\frac{32}{27}\\right)^2 + \\left(-\\frac{16}{9}\\right)^3 = \\frac{1024}{729} - \\frac{4096}{729} \\cdot \\frac{1}{...} = 0 \\]<\/p>\n<p>Como \\( \\Delta = 0 \\), a equa\u00e7\u00e3o tem uma raiz repetida. Com \\( \\sqrt[3]{-\\frac{q}{2}} = \\sqrt[3]{-\\frac{32}{27}} = -\\frac{4}{3} \\):<\/p>\n<p>\\[ t_1 = 2\\left(-\\frac{4}{3}\\right) = -\\frac{8}{3}, \\qquad t_2 = t_3 = -\\left(-\\frac{4}{3}\\right) = \\frac{4}{3} \\]<\/p>\n<p>Retro-substituindo \\( x = t - \\frac{8}{3} \\):<\/p>\n<p>\\[ x_1 = -\\frac{8}{3} - \\frac{8}{3} = 0, \\qquad x_2 = x_3 = \\frac{4}{3} - \\frac{8}{3} = -4 \\]<\/p>\n<p><strong>Resultado:<\/strong> \\( x_1 = 0 \\), \\( x_2 = -4 \\), \\( x_3 = -4 \\). Pode confirmar isto por fatora\u00e7\u00e3o: \\( x^3 + 8x^2 + 16x = x(x+4)^2 \\).<\/p>\n<p>\n\r\n<\/section>\n<h2>Como Usar a Calculadora<\/h2>\n<ol>\n<li>Introduza o <strong>Coeficiente a<\/strong> (o n\u00famero que multiplica \\( x^3 \\)). N\u00e3o pode ser 0 \u2014 caso contr\u00e1rio a equa\u00e7\u00e3o n\u00e3o \u00e9 c\u00fabica e a calculadora mostra um erro.<\/li>\n<li>Introduza o <strong>Coeficiente b<\/strong>, o multiplicador de \\( x^2 \\).<\/li>\n<li>Introduza o <strong>Coeficiente c<\/strong>, o multiplicador de \\( x \\).<\/li>\n<li>Introduza o <strong>Coeficiente d<\/strong>, o termo constante. Use 0 se a equa\u00e7\u00e3o n\u00e3o tem constante (como em \\( x^3 + 8x^2 + 16x = 0 \\)).<\/li>\n<li>Leia os resultados: <strong>Raiz x\u2081<\/strong>, <strong>Raiz x\u2082<\/strong> e <strong>Raiz x\u2083<\/strong>. Se a equa\u00e7\u00e3o tem apenas uma solu\u00e7\u00e3o real, os outros dois campos mostram \u00abRaiz complexa\u00bb, pois as duas ra\u00edzes restantes s\u00e3o complexas conjugadas.<\/li>\n<\/ol>\n<h2>O Que \u00c9 uma Equa\u00e7\u00e3o C\u00fabica?<\/h2>\n<p>Uma equa\u00e7\u00e3o c\u00fabica \u00e9 qualquer equa\u00e7\u00e3o polinomial de grau tr\u00eas, escrita na forma padr\u00e3o \\( ax^3 + bx^2 + cx + d = 0 \\) com \\( a \\neq 0 \\). Toda a equa\u00e7\u00e3o c\u00fabica com coeficientes reais tem pelo menos uma raiz real e no m\u00e1ximo tr\u00eas. Ao contr\u00e1rio de uma <a href=\"https:\/\/wpcalc.com\/pt\/matematica\/equacao-quadratica\/\">equa\u00e7\u00e3o quadr\u00e1tica<\/a>, que pode ser resolvida com uma \u00fanica f\u00f3rmula compacta, uma c\u00fabica exige fatora\u00e7\u00e3o, o m\u00e9todo de Cardano ou uma abordagem num\u00e9rica \u2014 por isso uma ferramenta de resolu\u00e7\u00e3o poupa tanto tempo.<\/p>\n<p>A calculadora funciona eliminando primeiro o termo em \\( x^2 \\). A substitui\u00e7\u00e3o \\( x = t - \\frac{b}{3a} \\) transforma qualquer c\u00fabica numa <em>c\u00fabica reduzida<\/em> \\( t^3 + pt + q = 0 \\), uma forma mais simples conhecida desde o s\u00e9culo XVI. A f\u00f3rmula de Cardano calcula ent\u00e3o uma grandeza an\u00e1loga ao discriminante, \\( \\Delta \\), que revela a natureza das ra\u00edzes antes mesmo de elas serem calculadas: uma raiz real mais duas complexas quando \\( \\Delta &gt; 0 \\), todas reais com uma raiz repetida quando \\( \\Delta = 0 \\), e tr\u00eas ra\u00edzes reais distintas quando \\( \\Delta &lt; 0 \\).<\/p>\n<p>Interpretar o resultado \u00e9 simples. Se as tr\u00eas ra\u00edzes forem n\u00fameros, o gr\u00e1fico de \\( y = ax^3 + bx^2 + cx + d \\) cruza o eixo x nesses pontos (tangenciando-o numa raiz repetida). Se dois campos mostrarem \u00abRaiz complexa\u00bb, o gr\u00e1fico cruza o eixo x apenas uma vez, na \u00fanica raiz real apresentada. As duas ra\u00edzes ocultas formam um <a href=\"https:\/\/wpcalc.com\/pt\/matematica\/conjugado-numero-complexo\/\">par de complexos conjugados<\/a>; pode explor\u00e1-las mais a fundo com a <a href=\"https:\/\/wpcalc.com\/pt\/matematica\/calculadora-numeros-complexos\/\">calculadora de n\u00fameros complexos<\/a>.<\/p>\n<p>As equa\u00e7\u00f5es c\u00fabicas aparecem em toda a matem\u00e1tica aplicada: encontrar pontos de interse\u00e7\u00e3o na geometria, calcular valores pr\u00f3prios na \u00e1lgebra linear, modelar problemas de volume na f\u00edsica e analisar estabilidade na engenharia e na economia.<\/p>\n<h2>Pressupostos, Limita\u00e7\u00f5es e Dicas<\/h2>\n<ul>\n<li><strong>O coeficiente a tem de ser diferente de zero.<\/strong> Se \\( a = 0 \\), a equa\u00e7\u00e3o \u00e9 na verdade quadr\u00e1tica (ou linear) \u2014 use o resolvedor de equa\u00e7\u00f5es quadr\u00e1ticas.<\/li>\n<li><strong>As ra\u00edzes complexas s\u00e3o assinaladas, n\u00e3o calculadas.<\/strong> A calculadora apresenta as ra\u00edzes reais numericamente e mostra \u00abRaiz complexa\u00bb para o par n\u00e3o real. Isto mant\u00e9m o resultado limpo para o uso quotidiano.<\/li>\n<li><strong>Arredondamento a 5 casas decimais.<\/strong> Os resultados s\u00e3o arredondados, pelo que uma raiz como \\( \\sqrt[3]{2} \\) aparece como 1,25992. Para a maioria dos fins, esta precis\u00e3o \u00e9 mais do que suficiente; podem surgir pequenas discrep\u00e2ncias se substituir uma raiz arredondada de volta na equa\u00e7\u00e3o.<\/li>\n<li><strong>Casos-limite num\u00e9ricos.<\/strong> Coeficientes muito grandes ou muito pequenos podem causar erros de arredondamento em v\u00edrgula flutuante, de modo que um discriminante matematicamente igual a zero pode ser calculado como um n\u00famero positivo ou negativo muito pequeno. Nesses casos, as ra\u00edzes apresentadas podem diferir nas \u00faltimas casas decimais.<\/li>\n<li><strong>Verifique com a regra de Descartes.<\/strong> Antes de resolver, pode estimar quantas ra\u00edzes reais positivas e negativas existem com a <a href=\"https:\/\/wpcalc.com\/pt\/matematica\/regra-dos-sinais-de-descartes\/\">calculadora da Regra dos Sinais de Descartes<\/a> e usar o resultado como verifica\u00e7\u00e3o do resultado do resolvedor. A acompanhar, a <a href=\"https:\/\/wpcalc.com\/pt\/matematica\/raiz-cubica\/\">calculadora de raiz c\u00fabica<\/a> \u00e9 \u00fatil quando s\u00f3 precisa de \\( \\sqrt[3]{n} \\) para um \u00fanico n\u00famero.<\/li>\n<li><strong>Fatora\u00e7\u00e3o simples primeiro.<\/strong> Verifique sempre se \\( x = 0 \\) \u00e9 raiz (ou seja, \\( d = 0 \\)) ou se um inteiro \u00f3bvio como 1, \u22121, 2 ou \u22122 satisfaz a equa\u00e7\u00e3o \u2014 extrair uma raiz reduz a c\u00fabica a uma quadr\u00e1tica que consegue resolver de cabe\u00e7a.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Resolve qualquer equa\u00e7\u00e3o c\u00fabica ax\u00b3 + bx\u00b2 + cx + d = 0 pelo m\u00e9todo de Cardano. Introduza os quatro coeficientes e a calculadora devolve as ra\u00edzes reais, assinala as complexas e deteta ra\u00edzes repetidas.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[16],"class_list":["post-232","post","type-post","status-publish","format-standard","hentry","category-matematica","tag-algebra"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/232","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/comments?post=232"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/232\/revisions"}],"predecessor-version":[{"id":1517,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/232\/revisions\/1517"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=232"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=232"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=232"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}