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ayırma zorunlu değil, direkt çözüm kümesini yazabilirsiniz.","İki kare farkı kullanarak çarpanlara ayırma yapılabilir veya denklemi eşitliğin diğer tarafına atarak da çözülebilir.","Paydada bulunan değerler çözüm kümesine alınmaz çünkü payda sıfır olamaz, bu durumda ifade tanımsız olur."]},"beginTime":599,"endTime":879,"href":"/video/preview/15739444939045824809?parent-reqid=1769754916632955-17812159446028343277-balancer-l7leveler-kubr-yp-klg-241-BAL&text=DerRedner90&t=599&ask_summarization=1"},{"index":7,"title":"Örnek Problemler","list":{"type":"unordered","items":["\"Üç katı karesinin on eksiğine eşit olan sayıların farkı kaç olabilir?\" sorusunda ikinci dereceden bir denklem elde edilir.","Denklemin çözüm kümesini bulurken önce pay kısmını çarpanlarına ayırıp kökleri bulur, sonra paydayı sıfır yapan değerleri kontrol ederiz.","Paydayı sıfır yapan değerler çözüm kümesine alınmaz, sadece payı sıfır yapan ve paydayı sıfır yapmayan değerler çözüm kümesine 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verilen bir değer vardır ve b² - 4ac formülüyle hesaplanır.","Delta, denklemin köklerinin varlığını belirler: Δ > 0 veya Δ = 0 olduğunda kökler vardır, Δ \u003c 0 olduğunda kök yoktur.","Δ > 0 olduğunda farklı iki reel kök vardır, Δ = 0 olduğunda aynı iki reel kök vardır, Δ \u003c 0 olduğunda reel kök yoktur."]},"beginTime":1534,"endTime":1745,"href":"/video/preview/15739444939045824809?parent-reqid=1769754916632955-17812159446028343277-balancer-l7leveler-kubr-yp-klg-241-BAL&text=DerRedner90&t=1534&ask_summarization=1"},{"index":10,"title":"İkinci Dereceden Denklemlerde Delta Kavramı","list":{"type":"unordered","items":["İkinci dereceden bir denklemin farklı iki reel kökü olması için delta (Δ) değeri sıfırdan büyük olmalıdır.","Δ = b² - 4ac formülü kullanılarak, m'nin alabileceği en büyük tam sayı değeri 6 olarak bulunmuştur.","m = 6 olduğunda delta sıfırdan büyük olurken, m = 7 olduğunda delta sıfıra eşit veya sıfırdan küçük 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paylaşılacaktır."]},"beginTime":2182,"endTime":2312,"href":"/video/preview/15739444939045824809?parent-reqid=1769754916632955-17812159446028343277-balancer-l7leveler-kubr-yp-klg-241-BAL&text=DerRedner90&t=2182&ask_summarization=1"},{"index":14,"title":"Formül Yöntemi Örneği","list":{"type":"unordered","items":["x² + 4x - 1 = 0 denkleminin çözümü için formül kullanılır.","Δ = b² - 4ac = 16 - 4(-1) = 20 hesaplanır.","Kökler x₁ = -2 + √5 ve x₂ = -2 - √5 olarak bulunur."]},"beginTime":2312,"endTime":2418,"href":"/video/preview/15739444939045824809?parent-reqid=1769754916632955-17812159446028343277-balancer-l7leveler-kubr-yp-klg-241-BAL&text=DerRedner90&t=2312&ask_summarization=1"},{"index":15,"title":"Tam Kareye Tamamlama Yöntemi","list":{"type":"unordered","items":["İkinci yöntem olan tam kareye tamamlama yöntemi de kullanılabilir.","x² + 4x - 1 = 0 denklemi (x+2)² - 5 = 0 şeklinde yazılır.","(x+2)² = 5 denkleminde x+2 = ±√5 olur ve kökler x₁ = -2 + √5, x₂ = -2 - √5 olarak bulunur."]},"beginTime":2418,"endTime":2476,"href":"/video/preview/15739444939045824809?parent-reqid=1769754916632955-17812159446028343277-balancer-l7leveler-kubr-yp-klg-241-BAL&text=DerRedner90&t=2418&ask_summarization=1"},{"index":16,"title":"Köklerle İlgili Yorumlar","list":{"type":"unordered","items":["Denklemin kökleri ile ilgili yorum yapmak için Δ (delta) değerine bakılır.","Δ = (a+2)² - 4a = (a-2)² olduğundan, Δ ya sıfıra eşit ya da sıfırdan büyüktür.","Δ = 0 olduğunda çift katlı kök, Δ > 0 olduğunda farklı iki kök vardır."]},"beginTime":2476,"endTime":2649,"href":"/video/preview/15739444939045824809?parent-reqid=1769754916632955-17812159446028343277-balancer-l7leveler-kubr-yp-klg-241-BAL&text=DerRedner90&t=2476&ask_summarization=1"},{"index":17,"title":"Örnek Problemler","list":{"type":"unordered","items":["2x² + ax - 3 = 0 denkleminde Δ = 2a olduğunda a = 8 olarak bulunur.","Bir kökü -1 olan denklemin diğer kökü 6 olarak 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değeri soruluyor.","Çözüm kümesi 1 olduğu için delta=0 olmalı ve kök yerine yazarak denklem çözülebilir.","Öğrencilere denklem çözümlerinde bazı soruları kendilerinin çözmeleri tavsiye ediliyor."]},"beginTime":3020,"endTime":3210,"href":"/video/preview/15739444939045824809?parent-reqid=1769754916632955-17812159446028343277-balancer-l7leveler-kubr-yp-klg-241-BAL&text=DerRedner90&t=3020&ask_summarization=1"},{"index":20,"title":"Kampın Devam Planı ve Motivasyon","list":{"type":"unordered","items":["Matematik kampının doksan gününün birinci haftası tamamlanmış durumda.","Yarın ikinci dereceden denklemler konusuna devam edilecek.","Öğrencilere motivasyon verilerek, güçlü başladıkları için doksan günden sonra kendilerini kontrol edemeyecekleri 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