{"paper":{"id":"site-4917","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":4,"source_label":"Matematyka · Zbiory zadań (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-4917/zad/5347","paper_id":"site-4917","number":"5347","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","text":"Dane jest równanie kwadratowe x^2-(3m+2)x+2m^2+7m-15=0 z niewiadomą x. Wyznacz wszystkie wartości parametru m, dla których różne rozwiązania x_1 i x_2 tego równania istnieją i spełniają warunek 2x_1^2 + 5x_1x_2 + 2x_2^2 = 2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4917/zad-5347.svg","solution_image":"img/site/4917/rozw-5347.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4917/zad/5513","paper_id":"site-4917","number":"5513","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","text":"Rozwiązywanie zadania. Wyznacz wszystkie wartości parametru a, dla których równanie x^2 - 2ax+ a^3 - 2a = 0 ma dwa różne rozwiązania dodatnie.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4917/zad-5513.svg","solution_image":"img/site/4917/rozw-5513.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4917/zad/6683","paper_id":"site-4917","number":"6683","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","text":"Dane jest równanie (x-6)⋅[(m-2)x² - 4(m+3)x + m+1] = 0 z niewiadomą x i parametrem m∈R. Wyznacz wszystkie wartości parametru m, dla których to równanie ma trzy różne rozwiązania rzeczywiste tego samego znaku.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4917/zad-6683.svg","solution_image":"img/site/4917/rozw-6683.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4917/zad/6835","paper_id":"site-4917","number":"6835","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"rozszerzona","text":"Wyznacz wszystkie wartości parametru m, dla których równanie x^2-(m-4)x + m^2-7m+12 = 0 ma dwa różne rozwiązania rzeczywiste x_1 oraz x_2, spełniające warunek x_1³ + x_2³ < 5x_1²⋅ x_2 + 5x_1⋅ x_2²","answer":null,"answer_text":null,"solution":null,"image":"img/site/4917/zad-6835.svg","solution_image":"img/site/4917/rozw-6835.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}