test","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=532&top_left_y=531&width=532&height=246&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab320862","slug":"let-fx-xsup2sup-bx-c-where-b-c-r-if-fx-is-a-factor","content":"Let f(x) = x² + bx + c where b, c Ī R. If f(x) is a factor of both x⁴ + 6x²+ 25 and 3x⁴ + 4x² +28x +5 then the least value of f(x) is","options":[{"_id":"68a3cd807f15af4716c3add2","text":"2","sequence":0,"isCorrect":false},{"_id":"68a3cd807f15af4716c3add3","text":"3","sequence":1,"isCorrect":false},{"_id":"68a3cd807f15af4716c3add4","text":"5/2","sequence":2,"isCorrect":false},{"_id":"68a3cd807f15af4716c3add5","text":"4","sequence":3,"isCorrect":true}],"correct_answer":"4","explanation":"f(x) will also be factor of\n\n3(x⁴ + 6x² + 25) – (3x⁴ + 4x² + 28x + 5)\n\n= 14 (x² – 2x + 5)\n\nIt means x² – 2x + 5 & x² + bx + c have both roots common\n\nHence least value of\n\nf(x) = (x – 1)² + 4 ³ 4","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.883Z","__v":0,"vector_store_id":"8d8407e2-7499-40be-b8db-d172a505c8cf","updated_at":"2024-08-30T21:49:39.883Z","isStarred":false},"params":{"questionSlug":"let-fx-xsup2sup-bx-c-where-b-c-r-if-fx-is-a-factor"}}]}]]

Question: Let f(x) = x<sup>2</sup> + bx + c where b, c Ī R. If f(x) is a factor of both x<sup>4</sup> + 6x<sup...

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