st","extracted_subject":"MATH","extracted_chapter":"QUADRATIC EQUATIONS","extracted_topic":"SOLUTION OF QUADRATIC EQUATIONS AND NATURE OF ROOTS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2141.png?top_left_x=0&top_left_y=1473&width=532&height=243&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab320857","slug":"if-both-roots-of-the-equation-xsup2sup-6ax-2-2a-9a","content":"If both roots of the equation x² – 6ax + 2 –2a + 9a² = 0, exceed 3, then a is-","options":[{"_id":"68aa864b7f15af4716d9fd1d","text":"Less than 11/9","sequence":0,"isCorrect":false},{"_id":"68aa864b7f15af4716d9fd1e","text":"Greater than 7/9","sequence":1,"isCorrect":false},{"_id":"68aa864b7f15af4716d9fd1f","text":"Greater than 5/9","sequence":2,"isCorrect":false},{"_id":"68aa864b7f15af4716d9fd20","text":"Greater than 11/9","sequence":3,"isCorrect":true}],"correct_answer":"Greater than 11/9","explanation":"(i) D ³ 0 (ii) (1) f(3) \\> 0 (iii) \\(\\frac{- b}{2a}\\)\\> 3\n\n(i) 36a² – 4(2 –2a + 9a²) ³ 0\n\na ³ 1 …(1)\n\n(ii) (1) (9 – 18a + 2 – 2a + 9a²) \\> 0 (9a – 11) (a –1) \\> 0\n\na Ī (– , 1) Č (11/9, ) … (2)\n\n(iii) \\(\\frac{- ( - 6a)}{2(1)}\\)\\> 3 a \\> 1 … (3)\n\nso, from (1), (2) and (3) a \\> 11/9","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.882Z","__v":0,"vector_store_id":"2f2c5be6-7427-483a-b504-676e29e9112f","updated_at":"2024-08-30T21:49:39.882Z","isStarred":false},"params":{"questionSlug":"if-both-roots-of-the-equation-xsup2sup-6ax-2-2a-9a"}}]}]]

Question: If both roots of the equation x<sup>2</sup> – 6ax + 2 –2a + 9a<sup>2</sup> = 0, exceed 3, then a is-...

Solution