{"id":2885,"date":"2022-05-15T13:18:04","date_gmt":"2022-05-15T11:18:04","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-s-komplexnimi-cisly\/"},"modified":"2022-05-15T14:44:14","modified_gmt":"2022-05-15T12:44:14","slug":"rovnice-s-komplexnimi-cisly","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-s-komplexnimi-cisly\/","title":{"rendered":"Kvadratick\u00e1 rovnice (b=0) &#8211; \u0159e\u0161en\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p>Pokud \u0159e\u0161\u00edme kvadratickou rovnici<em> <strong>ax\u00b2+bx+c=0<\/strong><\/em>, ve kter\u00e9 <strong><em>b=0<\/em><\/strong>, m\u016f\u017eeme si u\u0161et\u0159it v\u00fdpo\u010det diskriminantu a vyu\u017e\u00edt rychlej\u0161\u00edho \u0159e\u0161en\u00ed.<\/p>\n<ul>\n<li>poj\u010fme se na \u0159e\u0161en\u00ed pod\u00edvat nejprve teoreticky a n\u00e1sledn\u011b si jej vyzkou\u0161\u00edme v praxi<\/li>\n<li>v p\u0159\u00edpad\u011b, \u017ee :<\/li>\n<\/ul>\n<p>$$ax^2+bx+c=0, kde b=0$$<\/p>\n<p style=\"text-align: center\">m\u016f\u017eeme rovnice p\u0159epsat jako<\/p>\n<p>$$ax^2+c=0$$<\/p>\n<p style=\"text-align: center\">pokud budeme cht\u00edt vyj\u00e1d\u0159it<strong><em> x<\/em><\/strong>, jednodu\u0161e p\u0159esuneme <strong><em>c<\/em><\/strong> na druhou stranu a dostaneme:<\/p>\n<p>$$ax^2=-c$$<\/p>\n<p style=\"text-align: center\">zbav\u00edme se &#8220;\u00e1\u010dka&#8221;, respektive j\u00edm celou rovnici vyd\u011bl\u00edme a dostaneme:<\/p>\n<p>$$x^2=-\\frac{c}{a}$$<\/p>\n<ul>\n<li>V praxi tedy \u0159e\u0161en\u00ed takov\u00e9ho p\u0159\u00edkladu vypad\u00e1 n\u00e1sledovn\u011b:<\/li>\n<\/ul>\n<p>$$x^2+5=0$$<\/p>\n<p>$$x^2=-5$$<\/p>\n<p style=\"text-align: center\">pokud si uv\u011bdom\u00edme, \u017ee:<\/p>\n<p>$$i^2=-1$$<\/p>\n<p style=\"text-align: center\">m\u016f\u017eeme na\u0161\u00ed rovnici p\u0159epsat pr\u00e1v\u011b s pomoc\u00ed <em><strong>i\u00b2<\/strong><\/em><\/p>\n<p>$$5i^2=-5$$<\/p>\n<p style=\"text-align: center\">po drobn\u00e9 \u00faprav\u011b z\u00edsk\u00e1me v\u00fdsledek:<\/p>\n<p>$${i\\sqrt5}^2=-5$$<\/p>\n<p>$$x_1=i\\sqrt5$$<\/p>\n<p>$$x_2=-i\\sqrt5$$<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2885","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Kvadratick\u00e1 rovnice (b=0) - \u0159e\u0161en\u00fd p\u0159\u00edklad | Studijni-svet.cz<\/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:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-s-komplexnimi-cisly\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Kvadratick\u00e1 rovnice (b=0) - \u0159e\u0161en\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Pokud \u0159e\u0161\u00edme kvadratickou rovnici ax\u00b2+bx+c=0, ve kter\u00e9 b=0, m\u016f\u017eeme si u\u0161et\u0159it v\u00fdpo\u010det diskriminantu a vyu\u017e\u00edt rychlej\u0161\u00edho \u0159e\u0161en\u00ed. poj\u010fme se na \u0159e\u0161en\u00ed pod\u00edvat nejprve teoreticky a n\u00e1sledn\u011b si jej vyzkou\u0161\u00edme v praxi v p\u0159\u00edpad\u011b, \u017ee : $$ax^2+bx+c=0, kde b=0$$ m\u016f\u017eeme rovnice p\u0159epsat jako $$ax^2+c=0$$ pokud budeme cht\u00edt vyj\u00e1d\u0159it x, jednodu\u0161e p\u0159esuneme c na druhou stranu a ... 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