test","extracted_subject":"MATH","extracted_chapter":"COMPLEX NUMBERS","extracted_topic":"DE MOIVRE'S THEOREM AND ROOTS OF UNITY","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2137.png?top_left_x=1064&top_left_y=0&width=532&height=215&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab32078a","slug":"if-x-w-wsup2sup-2-then-the-value-of-xsup4sup-3xsup","content":"If x = w – w² – 2, then the value of x⁴ + 3x³ + 2x² – 11x – 6 is","options":[{"_id":"68a406427f15af4716c8bc72","text":"1","sequence":0,"isCorrect":true},{"_id":"68a406427f15af4716c8bc73","text":"– 1","sequence":1,"isCorrect":false},{"_id":"68a406427f15af4716c8bc74","text":"2","sequence":2,"isCorrect":false},{"_id":"68a406427f15af4716c8bc75","text":"4","sequence":3,"isCorrect":false}],"correct_answer":"1","explanation":"**Sol**. x+ 2 = w – w² ̃ x² + 4x+ 7 = 0\n\ndividing x⁴ +3x³ + 2x² – 11x – 6 by x² + 4x + 7 we get,\n\nx⁴ + 3x³ + 2x² – 11x – 6 = (x² + 4x + 7) (x² –x– 1) = 0 + 1 = 1","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.834Z","__v":0,"vector_store_id":"69b977e3-1440-45af-9cdb-26805e8f2fd3","updated_at":"2024-08-30T21:49:39.834Z","isStarred":false},"params":{"questionSlug":"if-x-w-wsup2sup-2-then-the-value-of-xsup4sup-3xsup"}}]}]]

Question: If x = w – w<sup>2</sup> – 2, then the value of x<sup>4</sup> + 3x<sup>3</sup> + 2x<sup>2</sup> – 11...

Solution