st","extracted_subject":"MATH","extracted_chapter":"QUADRATIC EQUATIONS","extracted_topic":"RELATION BETWEEN ROOTS AND COEFFICIENTS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2154.png?top_left_x=532&top_left_y=650&width=532&height=279&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab320a11","slug":"if-are-the-roots-of-axsup2sup-2bx-c-0-then-sup3sup","content":"If α, β are the roots of ax² – 2bx + c = 0, then\n\nα³β³ + α²β³ + α³β² is –","options":[{"_id":"68a37ba77f15af4716b63cb5","text":"\$\\frac{c^{2}(c + 2b)}{a^{3}}\$","sequence":0,"isCorrect":true},{"_id":"68a37ba77f15af4716b63cb6","text":"\$\\frac{bc^{3}}{a^{3}}\$","sequence":1,"isCorrect":false},{"_id":"68a37ba77f15af4716b63cb7","text":"\$\\frac{c^{2}}{a^{3}}\$","sequence":2,"isCorrect":false},{"_id":"68a37ba77f15af4716b63cb8","text":"None of thes","sequence":3,"isCorrect":false}],"correct_answer":"$$\\frac{c^{2}(c + 2b)}{a^{3}}$","explanation":"α + β = \$\\frac{2b}{a}\$, αβ = \$\\frac{c}{a}\$\n\nα³β³ + α²β³ + α³β² = (c/a)³ + (c/a)² (2b/a)\n\n= \$\\frac{c^{2}}{a^{3}}\$ [c + 2b]","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.985Z","__v":0,"vector_store_id":"db890909-e883-4620-ac75-532afeaa33b4","updated_at":"2024-08-30T21:49:39.985Z","isStarred":false},"params":{"questionSlug":"if-are-the-roots-of-axsup2sup-2bx-c-0-then-sup3sup"}}]}]]

Question: If α, β are the roots of ax<sup>2</sup> – 2bx + c = 0, then α<sup>3</sup>β<sup>3</sup> + α<sup>2</s...

Solution