{"id":668,"date":"2012-04-01T17:16:43","date_gmt":"2012-04-01T16:16:43","guid":{"rendered":"http:\/\/nosolomates.es\/?page_id=668"},"modified":"2012-04-01T17:16:43","modified_gmt":"2012-04-01T16:16:43","slug":"ecuaciones-de-2%c2%ba-grado","status":"publish","type":"page","link":"https:\/\/nosolomates.es\/?page_id=668","title":{"rendered":"Ecuaciones de 2\u00ba grado"},"content":{"rendered":"<p>Herramienta para resolver ecuaciones de segundo grado. Introduce los coeficientes en las cajas y pulsa &#8220;Calcular&#8221;.<\/p>\n<p><center><\/p>\n<div id=\"utilidades\"><h7><iframe loading=\"lazy\" src=\"web\/ecu2grado.htm\" width=\"470\" height=\"290\" scrolling=\"auto\" frameborder=\"0\"><\/p>\n<p>Texto alternativo para browsers que no aceptan iframes.<\/p>\n<p>    <\/iframe><\/h7><\/div>\n<p><\/center><br \/>\n<\/p>\n<h1>Explicaci\u00f3n:<\/h1>\n<p><\/p>\n<p>Una ecuaci\u00f3n de segundo grado es aquella cuyo t\u00e9rmino de grado mayor es 2. La forma general de estas ecuaciones es, una vez simplificada y pasados todos los t\u00e9rminos al primer miembro, de la siguiente forma:<\/p>\n<p><center><\/p>\n<p>ax<sup>2<\/sup> + bx + c = 0<\/p>\n<p><\/center><\/p>\n<p>donde a, b y c son los coeficientes.<\/p>\n<p>Resolviendo la ecuaci\u00f3n general por el m\u00e9todo de &#8220;completar cuadrados&#8221;, esto es, escribiendo el polinomio como el cuadrado de un binomio, se llega a la siguiente f\u00f3rmula, que es la que se utiliza para resolver este tipo de ecuaciones:<\/p>\n<p><center><img decoding=\"async\" src=\"web\/imagenes\/2grado.gif\"><\/center><\/p>\n<p>Esto da, en principio, dos soluciones (la positiva y la negativa de la ra\u00edz), que ser\u00e1n reales si el discriminante (b<sup>2<\/sup> &#8211; 4\u00b7a\u00b7c) es positivo, o complejas si es negativo. En el caso de que el discriminante sea cero, las dos soluciones de la ecuaci\u00f3n son la misma. En este caso se dice que la ecuaci\u00f3n tiene una soluci\u00f3n doble.<\/p>\n<p>Una vez halladas las soluciones x<sub>1<\/sub> y x<sub>2<\/sub>, es f\u00e1cil obtener la descomposici\u00f3n factorial del polinomio ax<sup>2<\/sup> + bx + c, ya que esta es a\u00b7(x &#8211; x<sub>1<\/sub>)\u00b7(x &#8211; x<sub>2<\/sub>), es decir:<\/p>\n<p><center><\/p>\n<p>ax<sup>2<\/sup> + bx + c = a\u00b7(x &#8211; x<sub>1<\/sub>)\u00b7(x &#8211; x<sub>2<\/sub>)<\/p>\n<p><\/center><\/p>\n<p>algo que resulta muy \u00fatil para simplificar fracciones algebr\u00e1icas, calcular dominios de funciones, etc.<\/p>\n<div><\/br>&nbsp;<\/div>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-official sd-sharing\"><div class=\"sd-content\"><ul><li class=\"share-facebook\"><div class=\"fb-share-button\" data-href=\"https:\/\/nosolomates.es\/?page_id=668\" data-layout=\"button_count\"><\/div><\/li><li class=\"share-twitter\"><a href=\"https:\/\/twitter.com\/share\" class=\"twitter-share-button\" data-url=\"https:\/\/nosolomates.es\/?page_id=668\" data-text=\"Ecuaciones de 2\u00ba grado\"  >Tweet<\/a><\/li><li class=\"share-linkedin\"><div class=\"linkedin_button\"><script type=\"in\/share\" data-url=\"https:\/\/nosolomates.es\/?page_id=668\" data-counter=\"right\"><\/script><\/div><\/li><li class=\"share-pinterest\"><div class=\"pinterest_button\"><a href=\"https:\/\/www.pinterest.com\/pin\/create\/button\/?url=https%3A%2F%2Fnosolomates.es%2F%3Fpage_id%3D668&#038;media=https%3A%2F%2Fsecure.gravatar.com%2Favatar%2Fc9ba1828908559b850337a4baa073367%3Fs%3D96%26d%3Dmm%26r%3Dg&#038;description=Ecuaciones%20de%202%C2%BA%20grado\" data-pin-do=\"buttonPin\" data-pin-config=\"beside\"><img src=\"\/\/assets.pinterest.com\/images\/pidgets\/pinit_fg_en_rect_gray_20.png\" \/><\/a><\/div><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Herramienta para resolver ecuaciones de segundo grado. Introduce los coeficientes en las cajas y pulsa &#8220;Calcular&#8221;. Texto alternativo para browsers que no aceptan iframes. Explicaci\u00f3n: Una ecuaci\u00f3n de segundo grado es aquella cuyo t\u00e9rmino de grado mayor es 2. La &hellip; <a href=\"https:\/\/nosolomates.es\/?page_id=668\">Sigue leyendo <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-official sd-sharing\"><div class=\"sd-content\"><ul><li class=\"share-facebook\"><div class=\"fb-share-button\" data-href=\"https:\/\/nosolomates.es\/?page_id=668\" data-layout=\"button_count\"><\/div><\/li><li class=\"share-twitter\"><a href=\"https:\/\/twitter.com\/share\" class=\"twitter-share-button\" data-url=\"https:\/\/nosolomates.es\/?page_id=668\" data-text=\"Ecuaciones de 2\u00ba grado\"  >Tweet<\/a><\/li><li class=\"share-linkedin\"><div class=\"linkedin_button\"><script type=\"in\/share\" data-url=\"https:\/\/nosolomates.es\/?page_id=668\" data-counter=\"right\"><\/script><\/div><\/li><li class=\"share-pinterest\"><div class=\"pinterest_button\"><a href=\"https:\/\/www.pinterest.com\/pin\/create\/button\/?url=https%3A%2F%2Fnosolomates.es%2F%3Fpage_id%3D668&#038;media=https%3A%2F%2Fsecure.gravatar.com%2Favatar%2Fc9ba1828908559b850337a4baa073367%3Fs%3D96%26d%3Dmm%26r%3Dg&#038;description=Ecuaciones%20de%202%C2%BA%20grado\" data-pin-do=\"buttonPin\" data-pin-config=\"beside\"><img src=\"\/\/assets.pinterest.com\/images\/pidgets\/pinit_fg_en_rect_gray_20.png\" \/><\/a><\/div><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"author":1,"featured_media":0,"parent":625,"menu_order":4,"comment_status":"open","ping_status":"open","template":"","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"jetpack_shortlink":"https:\/\/wp.me\/P9BfV-aM","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/668"}],"collection":[{"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/nosolomates.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=668"}],"version-history":[{"count":1,"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/668\/revisions"}],"predecessor-version":[{"id":669,"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/668\/revisions\/669"}],"up":[{"embeddable":true,"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/625"}],"wp:attachment":[{"href":"https:\/\/nosolomates.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}