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_2139.png?top_left_x=532&top_left_y=591&width=532&height=218&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab3207be","slug":"the-expression-fracx2-2x-1x2-2x-7-lies-in-the-inte","content":"The expression \\(\\frac{x^{2} + 2x + 1}{x^{2} + 2x + 7}\\) lies in the interval (x Ī R)","options":[{"_id":"68a939097f15af4716d3f3b0","text":"[0, – 1]","sequence":0,"isCorrect":false},{"_id":"68a939097f15af4716d3f3b1","text":"(–, 1) Č \\[1, )","sequence":1,"isCorrect":false},{"_id":"68a939097f15af4716d3f3b2","text":"\\[0, 1)","sequence":2,"isCorrect":true},{"_id":"68a939097f15af4716d3f3b3","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"\\[0, 1)","explanation":"Let y = x²+2x + 1/x ² + 2x + 7\n\nŽ x²(1– y) + 2x (1–y)+1–7y = 0, As x is real, so D ³ 0;\n\ni.e. 4(1 – y)² – 4(1 – y) (1 – 7y) ³ 0;\n\n1 + y²–2y–7y² + 8y – 1 ³ 0\n\nŽ – 6y² + 6y ³ 0 = y² – y £ 0\n\n\\\\ y Ī \\[0, 1) (As y ¹ 1)","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.839Z","__v":0,"vector_store_id":"22c7b828-c67f-438e-a3ea-5401a76fd3be","updated_at":"2024-08-30T21:49:39.839Z","isStarred":false},"params":{"questionSlug":"the-expression-fracx2-2x-1x2-2x-7-lies-in-the-inte"}}]}]]

Question: The expression \(\frac{x^{2} + 2x + 1}{x^{2} + 2x + 7}\) lies in the interval (x Ī R)...

Solution