{"id":346,"date":"2023-07-06T01:55:34","date_gmt":"2023-07-06T01:55:34","guid":{"rendered":"https:\/\/mathority.org\/pt\/trinomio\/"},"modified":"2023-07-06T01:55:34","modified_gmt":"2023-07-06T01:55:34","slug":"trinomio","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/trinomio\/","title":{"rendered":"Trin\u00f4mio"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o do que \u00e9 um trin\u00f4mio. Al\u00e9m disso, voc\u00ea poder\u00e1 ver os diferentes tipos de trin\u00f4mios existentes e, al\u00e9m disso, todas as f\u00f3rmulas relacionadas aos trin\u00f4mios.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-trinomio\"><\/span> O que \u00e9 um trin\u00f4mio?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Em matem\u00e1tica, a defini\u00e7\u00e3o de um trin\u00f4mio \u00e9 a seguinte:<\/p>\n<p> <strong>Um trin\u00f4mio \u00e9 um polin\u00f4mio composto por apenas tr\u00eas mon\u00f4mios<\/strong> . Em outras palavras, um trin\u00f4mio \u00e9 uma express\u00e3o alg\u00e9brica com apenas 3 termos diferentes conectados por um sinal de mais (+) ou menos (-). <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/trinome.png\" alt=\"o que significa um trin\u00f4mio\" class=\"wp-image-2905\" width=\"159\" height=\"159\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> A palavra trin\u00f4mio vem do grego e \u00e9 composta por dois componentes lexicais ( <em>tri<\/em> e <em>nomos<\/em> ), que significam o seguinte:<\/p>\n<ul>\n<li> <em>classificar<\/em> : prefixo que significa 3.<\/li>\n<li> <em>nomos<\/em> : significa parte.<\/li>\n<\/ul>\n<p> Podemos, portanto, deduzir o significado de trin\u00f4mio: polin\u00f4mio com tr\u00eas partes (ou tr\u00eas mon\u00f4mios).<\/p>\n<p> Por outro lado, voc\u00ea deve saber que muitas vezes \u00e9 muito \u00fatil fatorar um trin\u00f4mio. E para fatorar um polin\u00f4mio existem v\u00e1rios procedimentos como o m\u00e9todo de multiplica\u00e7\u00e3o FOIL ou a regra de Ruffini, mas quando \u00e9 um trin\u00f4mio \u00e9 feito mais rapidamente resolvendo uma equa\u00e7\u00e3o. Aprenda mais sobre este m\u00e9todo em <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\">como fatorar polin\u00f4mios de grau 2<\/a><\/span><\/strong> .<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-trinomios\"><\/span> Exemplos de trin\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para finalizar a compreens\u00e3o da no\u00e7\u00e3o de trin\u00f4mio, veremos v\u00e1rios exemplos desse tipo de polin\u00f4mio:<\/p>\n<ul>\n<li> Exemplo de trin\u00f4mio quadr\u00e1tico:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c62385e8cfd61050e46b1aeba0ce5459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-5x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<ul>\n<li> Exemplo de trin\u00f4mio de terceiro grau:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1ecc6c788bc20b31d875b39629faf8af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+4x^2+1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<ul>\n<li> Exemplo de trin\u00f4mio de quarto grau:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e406a5b6888dc32f4bc32908a3bb0c16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3x^4+x^2-8x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"120\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Agora que sabemos o que \u00e9 um trin\u00f4mio, veremos os diferentes tipos que existem e como resolver facilmente opera\u00e7\u00f5es com trin\u00f4mios usando f\u00f3rmulas. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Trinomio-cuadrado-perfecto\"><\/span> trin\u00f4mio quadrado perfeito<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Um <strong>trin\u00f4mio quadrado perfeito<\/strong> , por brevidade tamb\u00e9m chamado de <strong>TCP<\/strong> , \u00e9 o trin\u00f4mio obtido pela quadratura de um bin\u00f4mio, seja um bin\u00f4mio de adi\u00e7\u00e3o ou um bin\u00f4mio de subtra\u00e7\u00e3o. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/trinome-carre-parfait.png\" alt=\"complete o trin\u00f4mio quadrado perfeito\" class=\"wp-image-2553\" width=\"299\" height=\"300\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Portanto, um trin\u00f4mio quadrado perfeito \u00e9 composto por um polin\u00f4mio com dois quadrados perfeitos (sua raiz quadrada \u00e9 exata) e outro termo que \u00e9 o produto duplo das bases desses dois quadrados cujo sinal pode ser positivo ou negativo.<\/p>\n<p> Por outro lado, deve-se levar em conta que o quadrado de uma soma e o quadrado de uma diferen\u00e7a s\u00e3o identidades not\u00e1veis (ou produtos not\u00e1veis), portanto s\u00e3o duas f\u00f3rmulas amplamente utilizadas em matem\u00e1tica.<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo:<\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b1e801a4cc4d2bf8c8691b286cba38a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+6x+9\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Este exemplo \u00e9 um trin\u00f4mio quadrado perfeito porque em sua express\u00e3o alg\u00e9brica existem dois quadrados perfeitos, porque as ra\u00edzes quadradas de<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76e092d71026e8d64e9e3fc6857554cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p> e de 9 est\u00e3o corretos:.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-066a548275ed88e26557c66e450cee18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{x^2}=x\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -1px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5c9c78ea001d1be6abf9d9d58f232db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{9}=3\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> E, al\u00e9m disso, o \u00faltimo termo restante do trin\u00f4mio<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c74faf95634edd5ba7ba54895c9aea3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(6x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"31\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u00c9 obtido multiplicando as bases dos dois quadrados anteriores entre si e por 2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-96afb151877bff6626333e94ae128d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot x \\cdot 3 = 6x\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"96\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Portanto, toda a identidade not\u00e1vel neste exerc\u00edcio seria:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1b8a406baf500724d5a58e143cf05f0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+6x+9 =(x+3)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"174\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Se voc\u00ea olhar de perto, o que acabamos de fazer foi fatorar um trin\u00f4mio quadrado perfeito, porque fatoramos com sucesso a express\u00e3o trinomial. Ent\u00e3o, essas f\u00f3rmulas v\u00e3o te ajudar a fatorar um trin\u00f4mio quadrado perfeito, mas se voc\u00ea estiver interessado em fatorar qualquer outro tipo de trin\u00f4mio, recomendamos conferir o link acima na se\u00e7\u00e3o sobre <em>o que \u00e9 um trin\u00f4mio<\/em> (como fatorar polin\u00f4mios de grau 2) .<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Trinomio-al-cuadrado\"><\/span> trin\u00f4mio quadrado<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A f\u00f3rmula usada para calcular a pot\u00eancia de um trin\u00f4mio quadrado \u00e9: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/carre-dun-trinome.png\" alt=\"f\u00f3rmula para um trin\u00f4mio quadrado\" class=\"wp-image-2847\" width=\"378\" height=\"302\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Um <strong>trin\u00f4mio ao quadrado<\/strong> \u00e9 igual ao quadrado do primeiro termo, mais o quadrado do segundo termo, mais o quadrado do terceiro termo, mais duas vezes o primeiro termo, mais duas vezes o primeiro termo, mais duas vezes o segundo. o terceiro.<\/p>\n<p> Vejamos um exemplo de c\u00e1lculo do quadrado de um trin\u00f4mio:<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo:<\/h3>\n<ul>\n<li> Calcule o seguinte trin\u00f4mio elevado \u00e0 pot\u00eancia de 2:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ee4db6a5192b7efea2342d21275e487_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x^2+x+3\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"101\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> A f\u00f3rmula do quadrado de um trin\u00f4mio \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9597e2a9cf6403902d36e5ca6411045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"345\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ent\u00e3o, primeiro precisamos identificar os valores dos par\u00e2metros<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bfaed44949cf9cfbeb3445de33aabd3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a,b\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> da f\u00f3rmula. Neste exerc\u00edcio<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> Leste<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-09f6edd3d7af07ab26b4a0a71c20c0b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2,\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"22\" style=\"vertical-align: -4px;\"><\/p>\n<p> o coeficiente<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> corresponder ao<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-038741496726a75b03e91a2e030b0287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o termo independente 3:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-55e06f44486e75e9153a60d36e83bc37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} (a+b+c)^2\\\\[2ex] \\left(x^2+x+3\\right)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x^2 \\\\[2ex] b=x \\\\[2ex] c=3 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"90\" width=\"343\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> E quando j\u00e1 sabemos os valores, basta substituir esses valores na f\u00f3rmula e fazer os c\u00e1lculos: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-trinome-au-carre.png\" alt=\"exemplo de trin\u00f4mio quadrado\" class=\"wp-image-2850\" width=\"643\" height=\"224\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Trinomio-al-cubo\"><\/span> trin\u00f4mio ao cubo<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A f\u00f3rmula para encontrar a pot\u00eancia de um trin\u00f4mio ao cubo \u00e9 a seguinte: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/au-cube-du-trinome.png\" alt=\"trin\u00f4mio c\u00fabico homog\u00eaneo\" class=\"wp-image-2930\" width=\"448\" height=\"251\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Por exemplo, se quisermos calcular o seguinte trin\u00f4mio elevado \u00e0 pot\u00eancia de 3:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fb70975cf271ce076fb2377fb3844da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x^2+5x-3\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"110\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Voc\u00ea deve usar a f\u00f3rmula para o cubo de um trin\u00f4mio:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19b7d561533e65f35fa951a6fa29f2d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^3 = a^3+b^3+c^3+3(a+b)(a+c)(b+c)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"389\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A solu\u00e7\u00e3o para o problema seria, portanto: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e8e31df1b63350a57495a5d29237ff06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\left(x^2+5x-3\\right)^3 &amp; = \\left(x^2\\right)^3+(5x)^3+(-3)^3+3\\left(x^2+5x\\right)\\left(x^2+(-3)\\right)\\bigl(5x+\\left(-3\\right)\\bigr) \\\\[2ex] &amp; = x^6+125x^3-27+3\\left(x^4+5x^3-3x^2-15x\\right)\\bigl(5x-3\\bigr)\\\\[2ex] &amp; = x^6+125x^3-27+3\\left(5x^5+22x^4-30x^3-66x^2+45x\\right) \\\\[2ex] &amp; = x^6+125x^3-27+15x^5+66x^4-90x^3-198x^2+135x \\\\[2ex] &amp; = \\bm{x^6+15x^5+66x^4+35x^3-198x^2+135x-27}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"197\" width=\"602\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Trinomio-de-segundo-grado\"><\/span>trin\u00f4mio de segundo grau<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Em \u00e1lgebra, o <strong>trin\u00f4mio quadr\u00e1tico<\/strong> em uma vari\u00e1vel pode ser resolvido com a famosa f\u00f3rmula da equa\u00e7\u00e3o quadr\u00e1tica, que \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa907821a9aced835d381510935a2c24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"ax^2+bx+c=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"129\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9cdca238fce8ada66b67851d7bd9e044_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"165\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> A seguir, resolveremos um exerc\u00edcio trinomial quadr\u00e1tico como exemplo:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa91d7902d1dc20d7adc90f1593b1e0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-2x-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Na verdade, \u00e9 um trin\u00f4mio de segundo grau. Devemos, portanto, aplicar a f\u00f3rmula para a equa\u00e7\u00e3o quadr\u00e1tica:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9cdca238fce8ada66b67851d7bd9e044_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"165\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Devemos agora identificar o valor de cada inc\u00f3gnita:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o coeficiente do mon\u00f4mio de maior grau que neste caso vale 1,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> corresponde ao coeficiente do termo intermedi\u00e1rio que \u00e9 -2 e, por fim,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> representa o termo independente que \u00e9 -3.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8cd9d63de4b4941f033e58ae516bb35c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=1 \\qquad b=-2 \\qquad c=-3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"221\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ent\u00e3o, aplicamos a f\u00f3rmula substituindo os valores ali encontrados:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-478fd57bba865780094275d1d07eed4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-(-2) \\pm \\sqrt{(-2)^2 - 4\\cdot 1 \\cdot (-3)}}{2\\cdot 1}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"280\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> E, por fim, calculamos as opera\u00e7\u00f5es:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d1af7ce064d9ce80553bad53c51034ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x=\\cfrac{+2 \\pm \\sqrt{4 +12}}{2} = \\cfrac{2\\pm \\sqrt{16}}{2} = \\cfrac{2 \\pm 4}{2} = \\begin{cases} \\cfrac{2+4}{2}=3 \\\\[4ex] \\cfrac{2-4}{2} = -1 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"431\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> As solu\u00e7\u00f5es da equa\u00e7\u00e3o quadr\u00e1tica s\u00e3o, portanto: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e8c86a17e76085ddf1911e889e681c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = 3 \\qquad x=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"134\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o do que \u00e9 um trin\u00f4mio. Al\u00e9m disso, voc\u00ea poder\u00e1 ver os diferentes tipos de trin\u00f4mios existentes e, al\u00e9m disso, todas as f\u00f3rmulas relacionadas aos trin\u00f4mios. O que \u00e9 um trin\u00f4mio? Em matem\u00e1tica, a defini\u00e7\u00e3o de um trin\u00f4mio \u00e9 a seguinte: Um trin\u00f4mio \u00e9 um polin\u00f4mio composto por apenas tr\u00eas &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/trinomio\/\"> <span class=\"screen-reader-text\">Trin\u00f4mio<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[26],"tags":[],"class_list":["post-346","post","type-post","status-publish","format-standard","hentry","category-trinomios"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Trin\u00f4mio - Matoridade<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/trinomio\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Trin\u00f4mio - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o do que \u00e9 um trin\u00f4mio. 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Em matem\u00e1tica, a defini\u00e7\u00e3o de um trin\u00f4mio \u00e9 a seguinte: Um trin\u00f4mio \u00e9 um polin\u00f4mio composto por apenas tr\u00eas &hellip; Trin\u00f4mio Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/trinomio\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T01:55:34+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/trinome.png\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/trinomio\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/trinomio\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Trin\u00f4mio\",\"datePublished\":\"2023-07-06T01:55:34+00:00\",\"dateModified\":\"2023-07-06T01:55:34+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/trinomio\/\"},\"wordCount\":845,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Trin\u00f4mios\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/trinomio\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/trinomio\/\",\"url\":\"https:\/\/mathority.org\/pt\/trinomio\/\",\"name\":\"Trin\u00f4mio - Matoridade\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/#website\"},\"datePublished\":\"2023-07-06T01:55:34+00:00\",\"dateModified\":\"2023-07-06T01:55:34+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/pt\/trinomio\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/pt\/trinomio\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/pt\/trinomio\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Trin\u00f4mio\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/pt\/#website\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"name\":\"Mathority\",\"description\":\"Onde a curiosidade encontra o c\u00e1lculo!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/pt\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\",\"name\":\"Equipe Mathoridade\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Equipe Mathoridade\"},\"sameAs\":[\"http:\/\/mathority.org\/pt\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Trin\u00f4mio - Matoridade","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/pt\/trinomio\/","og_locale":"pt_BR","og_type":"article","og_title":"Trin\u00f4mio - Matoridade","og_description":"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o do que \u00e9 um trin\u00f4mio. 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