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Sınıf İkinci Dereceden Denklemler Test Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"İkinci Dereceden Denklemler Testi","list":{"type":"unordered","items":["Acil Matematik Ara Sınıf YouTube kanalında Sezgin Polat, 10. sınıf kış ödev köyünün 33. ve 35. sayfaları arasındaki ikinci dereceden denklemler testini çözecek."]},"beginTime":10,"endTime":24,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=10&ask_summarization=1"},{"index":1,"title":"Birinci Soru Çözümü","list":{"type":"unordered","items":["Verilen denklemin gerçek kökü olup olmadığını belirlemek için diskriminant (Δ) hesaplanır: Δ = b² - 4ac = (2n+1)² - 4(n+1) = 1.","Δ > 0 şeklinde olduğundan denklemin birbirinden farklı iki gerçek kökü vardır.","Kökler çarpımı c/a = (n+1)/(n+1) = 1 olduğundan, kökler çarpımı negatif değildir."]},"beginTime":24,"endTime":131,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=24&ask_summarization=1"},{"index":2,"title":"İkinci Soru Çözümü","list":{"type":"unordered","items":["Verilen denklemin köklerinden biri n olduğuna göre, n değeri denklemi sağlamalıdır.","Denklemde n yerine yazılıp sadeleştirildiğinde (2n²-1)=0 denklemi elde edilir.","Çözüm kümesi {-1/2, 1} olduğundan, n'nin alabileceği değerler toplamı 1/2'dir."]},"beginTime":131,"endTime":192,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=131&ask_summarization=1"},{"index":3,"title":"Üçüncü Soru Çözümü","list":{"type":"unordered","items":["Denklem çarpanlara ayrılamadığında, ikinci dereceden denklem formülü (x-x₁)(x-x₂) = 0 şeklinde kullanılır.","Δ = b² - 4ac = 36 - 8 = 28 olduğundan, kökler x₁ = -3 + √7 ve x₂ = -3 - √7 olarak bulunur."]},"beginTime":192,"endTime":300,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=192&ask_summarization=1"},{"index":4,"title":"Dördüncü Soru Çözümü","list":{"type":"unordered","items":["Denklem 3x² - 2x + 1 = 0 şeklinde yazılır ve diskriminant hesaplanır: Δ = 4 - 12 = -8.","Δ \u003c 0 olduğundan denklemin reel kökü yoktur.","Gerçek sayılarda çözüm kümesi boş kümedir."]},"beginTime":300,"endTime":343,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=300&ask_summarization=1"},{"index":5,"title":"Beşinci Soru Çözümü","list":{"type":"unordered","items":["Eşit sayıda oyuncusu bulunan iki takım bir sahada maç yapacaktır.","Herhangi bir takımda diskalifiyeler sonunda başlangıçtaki oyuncu sayısının bir fazlasının yarısı kadar oyuncu kalırsa maç sona erer.","Oyun dışı edilen oyuncu sayısıyla sağda kalan toplam oyuncu sayısının çarpımı tüm oyuncu sayısının üç katından iki fazladır."]},"beginTime":343,"endTime":399,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=343&ask_summarization=1"},{"index":6,"title":"İkinci Derece Denklemler Problemleri","list":{"type":"unordered","items":["Bir takımın oyuncu sayısının bir fazlasının yarısı kalıyorsa, diskalifiye edilen oyuncu sayısı x-1/2 olur ve sahada kalan oyuncu sayısı x+1/2 olur.","Diskalifiye edilen oyuncu sayısı ile sahada kalan toplam oyuncu sayısının çarpımı, tüm oyuncu sayısının üç katı olan 6x'ten 2 fazla olmalıdır.","Denklemin çözümü x=9 olarak bulunur, çünkü oyuncu sayısı negatif olamaz."]},"beginTime":402,"endTime":546,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=402&ask_summarization=1"},{"index":7,"title":"Denklemlerin Çözüm Kümesi","list":{"type":"unordered","items":["Verilen denklemin çözüm kümesi bir elemanlıdır çünkü çarpanlara ayrıldığında x=2/3 ve x=2/3 kökleri elde edilir.","İkinci derece denklemin birbirinden farklı iki reel kökü olması için m değeri -1'den farklı olmalı ve b²-4ac>0 olmalıdır.","Denklemin iki reel kökü olması için m değeri 0'dan büyük veya eşit olmalı ve b²-4ac≥0 olmalıdır."]},"beginTime":546,"endTime":733,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=546&ask_summarization=1"},{"index":8,"title":"Gerçek Sayılarda Kök Olmayan Denklemler","list":{"type":"unordered","items":["İkinci derece denklemin gerçek sayılarda kökü yoksa, diskriminantı sıfırdan küçük olmalıdır.","Denklemin gerçek sayılarda kökü yoksa, m'nin alabileceği en küçük tam sayı değeri 3'tür.","Sıvı sabun şişesi probleminde, bozuk olmayan durumda bir basımda akan sıvı miktarı 2x-5 gram olabilir."]},"beginTime":733,"endTime":974,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=733&ask_summarization=1"},{"index":9,"title":"Çakışık Kökler ve Diskriminant","list":{"type":"unordered","items":["Denklemin çakışık iki reel kökü olduğuna göre, diskriminant sıfıra eşit olmalıdır.","Denklemin köklerinin alabileceği farklı değerlerin toplamı 4'tür.","Denklemin kökleri en ve endir."]},"beginTime":974,"endTime":1212,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=974&ask_summarization=1"},{"index":10,"title":"Denklem Çözümü","list":{"type":"unordered","items":["Verilen denklemin kökleri en ve ense olarak belirtilmiştir.","Denklemde x yerine en ve ense değerleri yazılıp denklemin sağlanması sağlanmıştır.","İşlem sonucunda doğru cevap B şıkkı olarak bulunmuştur."]},"beginTime":1215,"endTime":1278,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=1215&ask_summarization=1"},{"index":11,"title":"Reel Sayılardaki Çözüm Kümesi","list":{"type":"unordered","items":["Verilen denklemin reel sayılardaki çözüm kümesi boş küme olduğundan, denklemin sıfırdan küçük olması gerekir.","Denklemde b²-4ac\u003c0 şeklinde yazılabilir ve 16=4k\u003c0 şeklinde sadeleştirilir.","k'nın alabileceği en küçük tam sayı değeri 5 olduğundan, doğru cevap C şıkkıdır."]},"beginTime":1278,"endTime":1312,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=1278&ask_summarization=1"},{"index":12,"title":"Analog Fotoğraf Makinesi Problemi","list":{"type":"unordered","items":["Analog fotoğraf makineleri 35 mm genişliğindeki şeritlerden oluşan 12, 24 veya 36 karelik pozlar kullanır.","Tuğba bir sayının iki katı kadar, Büşra ise aynı sayının karesinin dört fazlası kadar çekim yaptığında fotoğraf makinelerinde eşit sayıda karelik poz kalmaktadır.","Büşra'nın kullandığı karelik poz sayısı 20 olarak bulunmuştur."]},"beginTime":1312,"endTime":1488,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=1312&ask_summarization=1"},{"index":13,"title":"Diyafram Değerleri","list":{"type":"unordered","items":["Diyafram, fotoğraf makinelerinin objektiflerinde açılıp kısılarak filmi ulaşacak ışık miktarını ayarlayan iç içe geçmiş perde şeklindeki parçadır.","Her diyafram değeri artışında objektife giren ışık miktarı yarıya iner.","İbrahim'in makinesinde objektife düşen ışık miktarı, Masum'un makinesinde objektife düşen ışık miktarının 1/4 katıdır."]},"beginTime":1488,"endTime":1688,"href":"/video/preview/6770821459233398743?parent-reqid=1766688301281342-5232076233225676930-balancer-l7leveler-kubr-yp-klg-204-BAL&text=dev+dev+%C3%B6dev+33&t=1488&ask_summarization=1"},{"index":14,"title":"Denklemin Köklerinin Birer Eksiklerinin Kareleri Toplamı","list":{"type":"unordered","items":["Verilen denklemin kökleri a ve b olsun, kökler toplamı a+b=-2 ve kökler çarpımı a×b=-1'dir.","Köklerinin birer eksiklerinin kareleri toplamı (a-1)²+(b-1)² şeklinde hesaplanır.","İşlem sonucunda aranan değer 4 olarak 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