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_2142.png?top_left_x=0&top_left_y=1080&width=532&height=259&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab32085c","slug":"if-the-equation-axsup2sup-2bx-3c-0-have-no-real-ro","content":"If the equation ax² + 2bx – 3c = 0 have no real roots and\n\n4 (a + b) \\> 3c then","options":[{"_id":"68a3d2b27f15af4716c4d7dc","text":"c \\< 0","sequence":0,"isCorrect":true},{"_id":"68a3d2b27f15af4716c4d7dd","text":"c \\> 0","sequence":1,"isCorrect":false},{"_id":"68a3d2b27f15af4716c4d7de","text":"c ³ 0","sequence":2,"isCorrect":false},{"_id":"68a3d2b27f15af4716c4d7df","text":"c = 0","sequence":3,"isCorrect":false}],"correct_answer":"c \\< 0","explanation":"ax² + 2bx – 3c = 0 has no real roots\n\nŽ D \\< 0\n\nŽ 4b² + 12ac \\< 0 Ž b² + 3ac \\< 0\n\nAlso 4 (a + b) \\> 3c\n\nŽ 4a + 4b – 3 \\> 0 Ž f(2) \\> 0\n\nQ D \\< 0 then ax² + 2bx – 3c is either positive or negative \" x ĪR according to a \\> 0 or a \\< 0 but f(2) \\> 0,\n\n\\\\ f(x) \\> 0 \" x Ī R\n\nSo a \\> 0\n\nAlso f (0) \\> 0 Ž –3c \\> 0 Ž c \\< 0","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.882Z","__v":0,"vector_store_id":"94e51a33-ad99-42eb-bfb4-935f50a8c6f2","updated_at":"2024-08-30T21:49:39.882Z","isStarred":false},"params":{"questionSlug":"if-the-equation-axsup2sup-2bx-3c-0-have-no-real-ro"}}]}]]

Question: If the equation ax<sup>2</sup> + 2bx – 3c = 0 have no real roots and 4 (a + b) \> 3c then...

Solution