{"id":115,"date":"2023-07-16T22:47:33","date_gmt":"2023-07-16T22:47:33","guid":{"rendered":"https:\/\/mathority.org\/pt\/equacoes-quadraticas\/"},"modified":"2023-07-16T22:47:33","modified_gmt":"2023-07-16T22:47:33","slug":"equacoes-quadraticas","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/equacoes-quadraticas\/","title":{"rendered":"Como resolver equa\u00e7\u00f5es quadr\u00e1ticas?"},"content":{"rendered":"<p>Uma <strong>equa\u00e7\u00e3o quadr\u00e1tica ou equa\u00e7\u00e3o quadr\u00e1tica<\/strong> \u00e9 uma equa\u00e7\u00e3o de grau 2, com a qual o maior expoente de um de seus termos \u00e9 igual a 2. Isso significa que a equa\u00e7\u00e3o pode ter at\u00e9 duas solu\u00e7\u00f5es diferentes, embora tamb\u00e9m possa ter uma solu\u00e7\u00e3o \u00fanica ou Nenhum mesmo.<\/p>\n<p> Para calcular as solu\u00e7\u00f5es ou ra\u00edzes das equa\u00e7\u00f5es quadr\u00e1ticas, podemos seguir dois procedimentos diferentes: por meio da <strong>f\u00f3rmula quadr\u00e1tica<\/strong> ou <strong>pela fatora\u00e7\u00e3o da express\u00e3o<\/strong> . Neste artigo falaremos sobre os dois m\u00e9todos e daremos alguns exerc\u00edcios pr\u00e1ticos. Por\u00e9m antes vamos esclarecer alguns conceitos para que toda a explica\u00e7\u00e3o seja muito bem compreendida e voc\u00ea aproveite ao m\u00e1ximo a leitura.<\/p>\n<h2 id=\"tipos-de-ecuaciones-de-segundo-grado\" class=\"wp-block-heading\"> <span id=\"Tipos_de_ecuaciones_de_segundo_grado\">Tipos de equa\u00e7\u00f5es quadr\u00e1ticas<\/span><\/h2>\n<p> A principal categoriza\u00e7\u00e3o entre equa\u00e7\u00f5es quadr\u00e1ticas \u00e9 baseada na estrutura da pr\u00f3pria express\u00e3o. Assim, a estrutura padr\u00e3o ou usual destas express\u00f5es \u00e9 a seguinte: <strong>ax\u00b2 + bx + c<\/strong> . Essa forma comum \u00e9 equivalente a uma equa\u00e7\u00e3o completa, mas quando h\u00e1 termos nulos ou nulos, a estrutura pode variar, e \u00e9 a\u00ed que aparecem as equa\u00e7\u00f5es incompletas. A seguir explicaremos com mais detalhes as caracter\u00edsticas de todos os tipos.<\/p>\n<h3 id=\"ecuaciones-de-segundo-grado-completas\" class=\"wp-block-heading\"> Equa\u00e7\u00f5es quadr\u00e1ticas completas<\/h3>\n<p> Como j\u00e1 dissemos, temos as <strong>equa\u00e7\u00f5es quadr\u00e1ticas completas<\/strong> , estas possuem todos os coeficientes a, b e c diferentes de zero. A express\u00e3o segue, portanto, ao p\u00e9 da letra a estrutura ax\u00b2 + bx + c, pois possui todos os termos: o termo quadr\u00e1tico, o termo linear e o termo independente. Um exemplo desse tipo \u00e9 a seguinte equa\u00e7\u00e3o: x\u00b2 + 2x + 1 = 0.<\/p>\n<h3 id=\"ecuaciones-de-segundo-grado-incompletas\" class=\"wp-block-heading\"> Equa\u00e7\u00f5es quadr\u00e1ticas incompletas<\/h3>\n<p> Quanto \u00e0s equa\u00e7\u00f5es incompletas, podemos distingui-las de acordo com o coeficiente igual a zero. Lembre-se que se esta explica\u00e7\u00e3o n\u00e3o tirar suas d\u00favidas, logo abaixo est\u00e1 uma imagem na qual voc\u00ea encontra todos os casos explicados passo a passo.<\/p>\n<ul>\n<li> <strong>Equa\u00e7\u00f5es incompletas (b = 0):<\/strong> nesta primeira situa\u00e7\u00e3o encontramos uma express\u00e3o que segue a seguinte estrutura: ax\u00b2 + c = 0. Com a qual obtemos dois resultados: o negativo e o positivo da raiz da fra\u00e7\u00e3o c\/a .<\/li>\n<li> <strong>Equa\u00e7\u00f5es incompletas (c = 0):<\/strong> quando temos a forma ax\u00b2 + bx = 0 devemos fatorar a equa\u00e7\u00e3o para ter a express\u00e3o x (ax + b) = 0. Teremos portanto duas solu\u00e7\u00f5es: x = 0 e x = &#8211; BA.<\/li>\n<li> <strong>Equa\u00e7\u00f5es incompletas (b = c = 0):<\/strong> neste caso temos uma equa\u00e7\u00e3o ax\u00b2 = 0 e s\u00f3 temos uma solu\u00e7\u00e3o poss\u00edvel, que \u00e9 x = 0. <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-6482 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formules-equations-incompletes.webp\" sizes=\"auto, \" srcset=\"\" alt=\"f\u00f3rmulas equa\u00e7\u00f5es incompletas\" width=\"603\" height=\"312\" data-src=\"\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/01\/Formulas-ecuaciones-incompletas.png 603w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/01\/Formulas-ecuaciones-incompletas-500x259.png 500w\"><figcaption> resolu\u00e7\u00f5es explicadas<\/figcaption><\/figure>\n<\/div>\n<p> Vale ressaltar que os procedimentos que ensinamos permitem que voc\u00ea seja mais r\u00e1pido na resolu\u00e7\u00e3o de equa\u00e7\u00f5es incompletas. Mas, em todos os casos voc\u00ea pode usar a <strong>f\u00f3rmula quadr\u00e1tica<\/strong> que ensinaremos a seguir, bastando escrever zero nos coeficientes que n\u00e3o existem.<\/p>\n<h2 id=\"formula-para-ecuaciones-de-segundo-grado\" class=\"wp-block-heading\"> <span id=\"Formula_para_ecuaciones_de_segundo_grado\">F\u00f3rmula para equa\u00e7\u00f5es quadr\u00e1ticas<\/span><\/h2>\n<p> Para resolver equa\u00e7\u00f5es quadr\u00e1ticas (ax\u00b2 + bx + c = 0), precisamos aplicar a f\u00f3rmula geral ou f\u00f3rmula quadr\u00e1tica e depois precisamos <strong>substituir os valores num\u00e9ricos<\/strong> que correspondem a cada letra da express\u00e3o matem\u00e1tica. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-3185 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-dequation-quadratique.webp\" sizes=\"auto, \" srcset=\"\" alt=\"F\u00f3rmula para resolver equa\u00e7\u00f5es quadr\u00e1ticas\" width=\"445\" height=\"190\" data-src=\"\"><figcaption> F\u00f3rmula quadr\u00e1tica<\/figcaption><\/figure>\n<\/div>\n<p> Al\u00e9m disso, \u00e9 importante explicar que o <strong>discriminante (\u0394)<\/strong> \u00e9 a express\u00e3o b\u00b2 \u2013 4ac, que est\u00e1 localizada abaixo da raiz quadrada. A partir deste conceito matem\u00e1tico podemos saber quantas solu\u00e7\u00f5es esta equa\u00e7\u00e3o quadr\u00e1tica possui. Basicamente, existem tr\u00eas op\u00e7\u00f5es: o discriminante \u00e9 negativo (n\u00e3o existem solu\u00e7\u00f5es reais), o discriminante \u00e9 zero (existe apenas uma solu\u00e7\u00e3o) ou o discriminante \u00e9 positivo (existem duas solu\u00e7\u00f5es).<\/p>\n<h3 id=\"ejemplo-de-una-ecuacion-cuadratica-completa-resuelta\" class=\"wp-block-heading\"> Exemplo de uma equa\u00e7\u00e3o quadr\u00e1tica completa resolvida<\/h3>\n<p> Tente resolver a seguinte equa\u00e7\u00e3o quadr\u00e1tica: <strong>2x\u00b2+4x-6=0<\/strong> e compare seu resultado com o abaixo. Recomendamos que voc\u00ea siga o seguinte procedimento: analise o tipo de equa\u00e7\u00e3o (identifique os termos zero), calcule o discriminante para saber a quantidade de solu\u00e7\u00f5es existentes e por fim, resolva a equa\u00e7\u00e3o proposta com a f\u00f3rmula. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-3604 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/resolution-dequation-quadratique.webp\" sizes=\"auto, \" srcset=\"\" alt=\"Resolvendo Equa\u00e7\u00e3o Quadr\u00e1tica\" width=\"562\" height=\"403\" data-src=\"\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2021\/04\/Resolucion-de-ecuacion-de-segundo-grado.png 562w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2021\/04\/Resolucion-de-ecuacion-de-segundo-grado-500x359.png 500w\"><figcaption> Resolvendo uma equa\u00e7\u00e3o quadr\u00e1tica <\/figcaption><\/figure>\n<\/div>\n<h2 id=\"factorizar-ecuaciones-de-segundo-grado\" class=\"wp-block-heading\"> <span id=\"Factorizar_ecuaciones_de_segundo_grado\">Equa\u00e7\u00f5es quadr\u00e1ticas fatoriais<\/span><\/h2>\n<p> O segundo m\u00e9todo que temos para resolver equa\u00e7\u00f5es quadr\u00e1ticas \u00e9 <strong>a fatora\u00e7\u00e3o<\/strong> . Portanto, para <a href=\"https:\/\/mathority.org\/pt\/polinomios-fatoriais\/\" target=\"_blank\" rel=\"noreferrer noopener\">fatorar um polin\u00f4mio<\/a> (no nosso caso, um polin\u00f4mio quadr\u00e1tico), podemos usar diferentes m\u00e9todos. Embora em geral, quando se trata de equa\u00e7\u00f5es deste estilo, elas geralmente s\u00e3o fator\u00e1veis por um termo comum. E se n\u00e3o, voc\u00ea pode tentar aplicar <a href=\"https:\/\/mathority.org\/pt\" target=\"_blank\" rel=\"noreferrer noopener\">Notable Identities<\/a> , mas normalmente n\u00e3o precisar\u00e1 conhecer nenhum outro m\u00e9todo nessas situa\u00e7\u00f5es. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-6484 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equations-quadratiques-factorielles.webp\" sizes=\"auto, \" srcset=\"\" alt=\"Equa\u00e7\u00f5es quadr\u00e1ticas fatoriais\" width=\"294\" height=\"293\" data-src=\"\"><figcaption> equa\u00e7\u00e3o quadr\u00e1tica ponderada <\/figcaption><\/figure>\n<\/div>\n<h2 id=\"ejercicios-de-ecuaciones-de-segundo-grado-con-soluciones\" class=\"wp-block-heading\"> <span id=\"Ejercicios_de_ecuaciones_de_segundo_grado_con_soluciones\">Exerc\u00edcios de equa\u00e7\u00f5es quadr\u00e1ticas com solu\u00e7\u00f5es<\/span><\/h2>\n<p> Abaixo voc\u00ea encontrar\u00e1 uma s\u00e9rie de exerc\u00edcios sobre <strong>equa\u00e7\u00f5es quadr\u00e1ticas completas e incompletas<\/strong> . Assim voc\u00ea revisar\u00e1 toda a teoria explicada ao longo deste artigo e ficar\u00e1 mais claro como aplic\u00e1-la nos exerc\u00edcios. Recomendamos que voc\u00ea tente resolv\u00ea-los sozinho e s\u00f3 veja a solu\u00e7\u00e3o quando tiver conclu\u00eddo ou quando tiver d\u00favidas. Dito isto, voc\u00ea pode come\u00e7ar a resolver os exerc\u00edcios agora.<\/p>\n<h3 id=\"ejercicio-1\" class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Resolva a seguinte equa\u00e7\u00e3o quadr\u00e1tica: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-27\">\n<div class=\"wp-block-column is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-6487 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-quadratique-resolue.webp\" sizes=\"auto, \" srcset=\"\" alt=\"Equa\u00e7\u00e3o quadr\u00e1tica resolvida\" width=\"326\" height=\"411\" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<ol>\n<li> Come\u00e7amos calculando o discriminante, para saber o n\u00famero de solu\u00e7\u00f5es poss\u00edveis.<\/li>\n<li> Como esta \u00e9 uma equa\u00e7\u00e3o quadr\u00e1tica completa, aplicamos a f\u00f3rmula quadr\u00e1tica e resolvemos os c\u00e1lculos.<\/li>\n<li> Obtemos o valor da inc\u00f3gnita x.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h3 id=\"ejercicio-2\" class=\"wp-block-heading\"> Exerc\u00edcio 2<\/h3>\n<p> Resolva a seguinte equa\u00e7\u00e3o quadr\u00e1tica: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-30\">\n<div class=\"wp-block-column is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-6488 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-quadratique-incomplete.webp\" sizes=\"auto, \" srcset=\"\" alt=\"Equa\u00e7\u00e3o quadr\u00e1tica incompleta\" width=\"341\" height=\"368\" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<ol>\n<li> Come\u00e7amos calculando o discriminante.<\/li>\n<li> Como temos uma equa\u00e7\u00e3o quadr\u00e1tica incompleta em que b = 0, aplicamos o padr\u00e3o para equa\u00e7\u00f5es deste tipo.<\/li>\n<li> Resolvemos o c\u00e1lculo para obter o resultado, e n\u00e3o podemos esquecer do sinal \u00b1.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h3 id=\"ejercicio-3\" class=\"wp-block-heading\"> Exerc\u00edcio 3<\/h3>\n<p> Resolva a seguinte equa\u00e7\u00e3o quadr\u00e1tica n\u00e3o ordenada: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-33\">\n<div class=\"wp-block-column is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-6493 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-quadratique-non-ordonnee.webp\" sizes=\"auto, \" srcset=\"\" alt=\"Equa\u00e7\u00e3o quadr\u00e1tica n\u00e3o ordenada\" width=\"344\" height=\"522\" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<ol>\n<li> Come\u00e7amos calculando o discriminante da equa\u00e7\u00e3o.<\/li>\n<li> Antes de podermos aplicar a f\u00f3rmula, precisamos ordenar a equa\u00e7\u00e3o de acordo com a estrutura ax\u00b2 + bx + c = 0.<\/li>\n<li> Ent\u00e3o aplicamos a f\u00f3rmula geral.<\/li>\n<li> E finalmente obtemos os resultados.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h3 id=\"ejercicio-4\" class=\"wp-block-heading\"> Exerc\u00edcio 4<\/h3>\n<p> Resolva a seguinte equa\u00e7\u00e3o quadr\u00e1tica fatorando: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-36\">\n<div class=\"wp-block-column is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-6495 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-incomplete.webp\" sizes=\"auto, \" srcset=\"\" alt=\"equa\u00e7\u00e3o incompleta\" width=\"324\" height=\"467\" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<ol>\n<li> Primeiro calculamos o discriminante.<\/li>\n<li> A seguir, extra\u00edmos o fator comum de x.<\/li>\n<li> Portanto, a primeira solu\u00e7\u00e3o \u00e9 x = 0.<\/li>\n<li> E o segundo \u00e9 x = 3\/2.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h3 id=\"ejercicio-5\" class=\"wp-block-heading\"> Exerc\u00edcio 5<\/h3>\n<p> Resolva a equa\u00e7\u00e3o quadr\u00e1tica completa que mostramos abaixo: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-39\">\n<div class=\"wp-block-column is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-6496 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-quadratique-facile.webp\" sizes=\"auto, \" srcset=\"\" alt=\"Equa\u00e7\u00e3o Quadr\u00e1tica F\u00e1cil\" width=\"335\" height=\"505\" data-src=\"\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/01\/Ecuacion-de-segundo-grado-facil.png 335w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/01\/Ecuacion-de-segundo-grado-facil-332x500.png 332w\"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<ol>\n<li> Como sempre, calculamos o discriminante para descobrir quantas solu\u00e7\u00f5es a equa\u00e7\u00e3o em quest\u00e3o possui.<\/li>\n<li> A seguir, aplicamos a f\u00f3rmula quadr\u00e1tica, por se tratar de uma equa\u00e7\u00e3o completa.<\/li>\n<li> Finalmente, expressamos o resultado da equa\u00e7\u00e3o.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h3 id=\"ejercicio-6\" class=\"wp-block-heading\"> Exerc\u00edcio 6<\/h3>\n<p> Resolva a equa\u00e7\u00e3o quadr\u00e1tica com fra\u00e7\u00f5es que oferecemos: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-42\">\n<div class=\"wp-block-column is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-6497 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-quadratique-avec-fractions.webp\" sizes=\"auto, \" srcset=\"\" alt=\"Equa\u00e7\u00e3o quadr\u00e1tica com fra\u00e7\u00f5es\" width=\"380\" height=\"609\" data-src=\"\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/01\/Ecuacion-de-segundo-grado-con-fracciones.png 380w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/01\/Ecuacion-de-segundo-grado-con-fracciones-312x500.png 312w\"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<ol>\n<li> Come\u00e7amos calculando o discriminante da express\u00e3o.<\/li>\n<li> A seguir aplicamos a f\u00f3rmula quadr\u00e1tica, levando em considera\u00e7\u00e3o que o coeficiente \u201ca\u201d \u00e9 formado por uma fra\u00e7\u00e3o.<\/li>\n<li> Resolvemos o c\u00e1lculo.<\/li>\n<li> E j\u00e1 temos as duas ra\u00edzes da equa\u00e7\u00e3o.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h3 id=\"ejercicio-7\" class=\"wp-block-heading\"> Exerc\u00edcio 7<\/h3>\n<p> Resolva a seguinte equa\u00e7\u00e3o quadr\u00e1tica: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-45\">\n<div class=\"wp-block-column is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-6498 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-quadratique-difficile.webp\" sizes=\"auto, \" srcset=\"\" alt=\"Equa\u00e7\u00e3o quadr\u00e1tica de dificuldade\" width=\"473\" height=\"675\" data-src=\"\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/01\/Ecuacion-de-segundo-grado-dificil.png 473w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/01\/Ecuacion-de-segundo-grado-dificil-350x500.png 350w\"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<ol>\n<li> Come\u00e7amos calculando o discriminante.<\/li>\n<li> Antes de aplicar a f\u00f3rmula, precisamos simplificar a express\u00e3o e dar-lhe a forma ax\u00b2 + b + c = 0.<\/li>\n<li> Substitu\u00edmos todos os coeficientes na f\u00f3rmula e resolvemos o c\u00e1lculo.<\/li>\n<li> Finalmente obtemos o resultado.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h3 id=\"ejercicio-8\" class=\"wp-block-heading\"> Exerc\u00edcio 8<\/h3>\n<p> Prova de resolu\u00e7\u00e3o da seguinte equa\u00e7\u00e3o quadr\u00e1tica: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-48\">\n<div class=\"wp-block-column is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-6499 lazyload\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-dequations-quadratiques.webp\" sizes=\"auto, \" srcset=\"\" alt=\"Exerc\u00edcios de equa\u00e7\u00e3o quadr\u00e1tica\" width=\"490\" height=\"522\" data-src=\"\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/01\/Ejercicios-de-ecuaciones-de-segundo-grado.png 490w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/01\/Ejercicios-de-ecuaciones-de-segundo-grado-469x500.png 469w\"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<ol>\n<li> Come\u00e7amos calculando o discriminante.<\/li>\n<li> Como voc\u00ea pode ver, esta \u00e9 uma equa\u00e7\u00e3o quadr\u00e1tica simples, embora tenha coeficientes bastante grandes. Portanto, precisamos aplicar a f\u00f3rmula e ter cuidado ao realizar as opera\u00e7\u00f5es.<\/li>\n<li> No final, obtemos as duas solu\u00e7\u00f5es poss\u00edveis.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Uma equa\u00e7\u00e3o quadr\u00e1tica ou equa\u00e7\u00e3o quadr\u00e1tica \u00e9 uma equa\u00e7\u00e3o de grau 2, com a qual o maior expoente de um de seus termos \u00e9 igual a 2. Isso significa que a equa\u00e7\u00e3o pode ter at\u00e9 duas solu\u00e7\u00f5es diferentes, embora tamb\u00e9m possa ter uma solu\u00e7\u00e3o \u00fanica ou Nenhum mesmo. Para calcular as solu\u00e7\u00f5es ou ra\u00edzes das &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/equacoes-quadraticas\/\"> <span class=\"screen-reader-text\">Como resolver equa\u00e7\u00f5es quadr\u00e1ticas?<\/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":[14],"tags":[],"class_list":["post-115","post","type-post","status-publish","format-standard","hentry","category-explicacoes-matematicas"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Como resolver equa\u00e7\u00f5es quadr\u00e1ticas? -Maturidade<\/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\/equacoes-quadraticas\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como resolver equa\u00e7\u00f5es quadr\u00e1ticas? -Maturidade\" \/>\n<meta property=\"og:description\" content=\"Uma equa\u00e7\u00e3o quadr\u00e1tica ou equa\u00e7\u00e3o quadr\u00e1tica \u00e9 uma equa\u00e7\u00e3o de grau 2, com a qual o maior expoente de um de seus termos \u00e9 igual a 2. 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