{"json_modified": "2016-09-21T08:47:54.320565", "uuid": "a93e7b13-2506-484b-a178-126595fcbcec", "title": "MathML: Deriving the Quadratic Formula", "url": "/en-US/docs/Web/MathML/Examples/Deriving_the_Quadratic_Formula", "tags": ["Beginner", "Guide", "Example", "HTML5", "Education", "MathML", "beginner", "NeedsBeginnerUpdate"], "translations": [{"uuid": "5cdc34c4-a4a8-42bf-8362-4e252b5dad1d", "title": "L\u00f6sungsformel f\u00fcr die Quadratische Gleichung", "url": "/de/docs/Web/MathML/Beispiele/Quadratische_Gleichung", "tags": ["MathML", "Beispiel"], "summary": "L\u00f6sungsformel der Quadratischen Gleichung (mit quadratischer Erg\u00e4nzung)", "localization_tags": [], "locale": "de", "last_edit": "2016-01-05T04:26:44", "review_tags": []}, {"uuid": "9f4954ba-a16b-42ad-aa54-be2e4c1cda45", "title": "MathML: D\u00e9river la Formule Quadratique", "url": "/fr/docs/Web/MathML/Exemples/D%C3%A9river_la_Formule_Quadratique", "tags": ["D\u00e9butant", "Guide", "MathML", "HTML5", "Education"], "summary": "<math><mtable columnalign=\"left\"><mtr><mtd><mrow><mrow><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mi>a</mi><mo>\u2062</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo> + </mo><mi>b</mi><mo>\u2062</mo><mi>x</mi></mrow><mo> + </mo><mi>c</mi></mrow><mo>=</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mi>a</mi><mo>\u2062</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo> + </mo><mi>b</mi><mo>\u2062</mo><mi>x</mi><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/></mrow><mo>=</mo><mo>-</mo><mi> c</mi><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><msup><mi>x</mi><mn>2</mn></msup></mrow><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mi>a</mi></mfrac><mo>\u2064</mo><mi>x</mi></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mo>=</mo><mfrac><mrow><mo>-</mo><mi>c</mi></mrow><mi>a</mi></mfrac><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\">Diviser le premier coefficient.</mtext></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><msup><mi>x</mi><mn>2</mn></msup></mrow><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mi>a</mi></mfrac><mo>\u2064</mo><mi>x</mi><mo> + </mo><msup><mfenced><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mfenced><mn>2</mn></msup></mrow><mo>=</mo><mfrac><mrow><mo>-</mo><mi>c</mi><mo>(</mo><mn>4</mn><mi>a</mi><mo>)</mo></mrow><mrow><mi>a</mi><mo>(</mo><mn>4</mn><mi>a</mi><mo>)</mo></mrow></mfrac></mrow><mo> + </mo><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\">Compl\u00e8te le carr\u00e9</mtext></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mo>(</mo><mi>x</mi><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>)</mo><mo>(</mo><mi>x</mi><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>)</mo><mo>=</mo><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo> - </mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\">Discriminant r\u00e9v\u00e9l\u00e9</mtext></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>)</mo></mrow><mn>2</mn></msup><mo>=</mo><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo> - </mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\"/></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mrow><mi>x</mi><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow><mo>=</mo><msqrt><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo> - </mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></msqrt></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\"/></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mrow><mi>x</mi></mrow><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>\u00b1</mo><mrow><mo>{</mo><mi>C</mi><mo>}</mo></mrow><msqrt><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo> - </mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></msqrt></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\">Voici la formule du sommet</mtext></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mrow><mi>x</mi></mrow><mo>=</mo><mfrac><mrow><mo>-</mo><mi> b</mi><mo>\u00b1</mo><mrow><mo>{</mo><mi>C</mi><mo>}</mo></mrow><msqrt><msup><mi>b</mi><mn>2</mn></msup><mo> - </mo><mn>4</mn><mi>a</mi><mi>c</mi></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\"/></mrow></mrow></mtd></mtr></mtable></math>", "localization_tags": ["inprogress"], "locale": "fr", "last_edit": "2016-09-21T08:47:52", "review_tags": ["editorial"]}, {"uuid": "df00ba69-8641-4c61-b8ca-bc88efd2bc34", "title": "MathML: \u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u516c\u5f0f\u3092\u5c0e\u304f", "url": "/ja/docs/Web/MathML/Examples/Deriving_the_Quadratic_Formula", "tags": ["Beginner", "Guide", "NeedsBeginnerUpdate", "HTML5", "Education", "MathML"], "summary": "<math><mtable columnalign=\"left\"><mtr><mtd><mrow><mrow><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mi>a</mi><mo>\u2062</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo> + </mo><mi>b</mi><mo>\u2062</mo><mi>x</mi></mrow><mo> + </mo><mi>c</mi></mrow><mo>=</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mi>a</mi><mo>\u2062</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo> + </mo><mi>b</mi><mo>\u2062</mo><mi>x</mi><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/></mrow><mo>=</mo><mo>-</mo><mi> c</mi><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><msup><mi>x</mi><mn>2</mn></msup></mrow><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mi>a</mi></mfrac><mo>\u2064</mo><mi>x</mi></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mo>=</mo><mfrac><mrow><mo>-</mo><mi>c</mi></mrow><mi>a</mi></mfrac><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\">\u9996\u4f4d\u4fc2\u6570\u3067\u4e21\u8fba\u3092\u5272\u308b\u3002</mtext></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><msup><mi>x</mi><mn>2</mn></msup></mrow><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mi>a</mi></mfrac><mo>\u2064</mo><mi>x</mi><mo> + </mo><msup><mfenced><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mfenced><mn>2</mn></msup></mrow><mo>=</mo><mfrac><mrow><mo>-</mo><mi>c</mi><mo>(</mo><mn>4</mn><mi>a</mi><mo>)</mo></mrow><mrow><mi>a</mi><mo>(</mo><mn>4</mn><mi>a</mi><mo>)</mo></mrow></mfrac></mrow><mo> + </mo><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\">\u5e73\u65b9\u5b8c\u6210\u3002</mtext></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mo>(</mo><mi>x</mi><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>)</mo><mo>(</mo><mi>x</mi><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>)</mo><mo>=</mo><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo> - </mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\">\u5224\u5225\u5f0f\u304c\u73fe\u308c\u308b\u3002</mtext></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>)</mo></mrow><mn>2</mn></msup><mo>=</mo><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo> - </mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\"/></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mrow><mi>x</mi><mo> + </mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow><mo>=</mo><msqrt><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo> - </mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></msqrt></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\"/></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mrow><mi>x</mi></mrow><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>\u00b1</mo><mrow><mo>{</mo><mi>C</mi><mo>}</mo></mrow><msqrt><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo> - </mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></msqrt></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\">\u9802\u70b9\u3092\u6c42\u3081\u308b\u516c\u5f0f\u3002</mtext></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2.5ex\"/><mrow><mi>x</mi></mrow><mo>=</mo><mfrac><mrow><mo>-</mo><mi> b</mi><mo>\u00b1</mo><mrow><mo>{</mo><mi>C</mi><mo>}</mo></mrow><msqrt><msup><mi>b</mi><mn>2</mn></msup><mo> - </mo><mn>4</mn><mi>a</mi><mi>c</mi></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow><mspace depth=\"1ex\" height=\"0.5ex\" width=\"2ex\"/><mrow><mtext mathcolor=\"red\" mathsize=\"10pt\"/></mrow></mrow></mtd></mtr></mtable></math>", "localization_tags": [], "locale": "ja", "last_edit": "2016-01-20T05:03:56", "review_tags": []}], "modified": "2016-09-06T04:51:12", "label": "MathML: Deriving the Quadratic Formula", "localization_tags": [], "locale": "en-US", "id": 61763, "last_edit": "2016-09-06T04:51:11", "summary": "This page outlines the derivation of the Quadratic Formula.", "sections": [], "slug": "Web/MathML/Examples/Deriving_the_Quadratic_Formula", "review_tags": []}