{"id":2894,"date":"2022-05-15T13:39:30","date_gmt":"2022-05-15T11:39:30","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseni-kvadraticke-rovnice-se-zapornym-diskriminantem\/"},"modified":"2022-05-15T14:51:10","modified_gmt":"2022-05-15T12:51:10","slug":"reseni-kvadraticke-rovnice-se-zapornym-diskriminantem","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseni-kvadraticke-rovnice-se-zapornym-diskriminantem\/","title":{"rendered":"\u0158e\u0161en\u00ed kvadratick\u00e9 rovnice se z\u00e1porn\u00fdm diskriminantem"},"content":{"rendered":"<p>D\u00edky tomu, \u017ee ji\u017e zn\u00e1me komplexn\u00ed \u010d\u00edsla a um\u00edme s nimi pracovat, m\u016f\u017eeme vypo\u010d\u00edtat tak\u00e9 kvadratick\u00e9 rovnice, jejich\u017e <strong>diskriminant je z\u00e1porn\u00fd<\/strong><\/p>\n<ul>\n<li>pro v\u00fdpo\u010det ko\u0159en\u016f kvadratick\u00e9 rovnice, jejich\u017e <strong>diskriminant je z\u00e1porn\u00fd<\/strong> (<strong><em>D&lt;0<\/em><\/strong>), plat\u00ed:<\/li>\n<\/ul>\n<p>$$x_{1,2}=\\frac{-b\u00b1i\\sqrt{-D}}{2a}$$<\/p>\n<ul>\n<li>s t\u00edmto vzorcem v pam\u011bti se m\u016f\u017eeme vrhnout do \u0159e\u0161en\u00ed vzorov\u00e9ho p\u0159\u00edkladu:<\/li>\n<\/ul>\n<p>$$x^2-2x+5=0$$<\/p>\n<p style=\"text-align: center\">dosad\u00edme do vzorce pro v\u00fdpo\u010det diskriminantu<\/p>\n<p>&nbsp;<\/p>\n<p>$$D=b^2-4ac$$<\/p>\n<p>$$D=(-2)^2-4\\cdot5=4-20=-16$$<\/p>\n<p style=\"text-align: center\">diskriminant n\u00e1m vy\u0161el z\u00e1porn\u00fd, dosad\u00edme tedy do vzore pro ko\u0159eny rovnice pro <strong><em>D&lt;0:<\/em><\/strong><\/p>\n<p>$$x_{1,2}=\\frac{-b\u00b1i\\sqrt{-D}}{2a}=\\frac{-(-2)\u00b1i\\sqrt{-(-16)}}{2}=\\frac{2\u00b1i\\sqrt{16}}{2}=\\frac{2\u00b14i}{2}$$<\/p>\n<p style=\"text-align: center\">a z\u00edsk\u00e1me v\u00fdsledek:<\/p>\n<p>$$x_1=1+2i$$<\/p>\n<p>$$x_2=1-2i$$<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2894","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>\u0158e\u0161en\u00ed kvadratick\u00e9 rovnice se z\u00e1porn\u00fdm diskriminantem | 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\/reseni-kvadraticke-rovnice-se-zapornym-diskriminantem\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0158e\u0161en\u00ed kvadratick\u00e9 rovnice se z\u00e1porn\u00fdm diskriminantem | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"D\u00edky tomu, \u017ee ji\u017e zn\u00e1me komplexn\u00ed \u010d\u00edsla a um\u00edme s nimi pracovat, m\u016f\u017eeme vypo\u010d\u00edtat tak\u00e9 kvadratick\u00e9 rovnice, jejich\u017e diskriminant je z\u00e1porn\u00fd pro v\u00fdpo\u010det ko\u0159en\u016f kvadratick\u00e9 rovnice, jejich\u017e diskriminant je z\u00e1porn\u00fd (D&lt;0), plat\u00ed: $$x_{1,2}=frac{-b\u00b1isqrt{-D}}{2a}$$ s t\u00edmto vzorcem v pam\u011bti se m\u016f\u017eeme vrhnout do \u0159e\u0161en\u00ed vzorov\u00e9ho p\u0159\u00edkladu: $$x^2-2x+5=0$$ dosad\u00edme do vzorce pro v\u00fdpo\u010det diskriminantu &nbsp; $$D=b^2-4ac$$ $$D=(-2)^2-4cdot5=4-20=-16$$ ... 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