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dereceden denklemler, 10. sınıf matematik, İkinci dereceden denklemler sibel hoca, ile başlıyoruz. Matematik problemleri, nde başarılı olabilmek için bilmemiz gereken en temel matematik...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3585564/c1fdedaba678d645d781ad7e090b813e/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/TZJ_fQAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"1","reqid":"1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=videoid:1130392608741864006","teaser":[{"list":{"type":"unordered","items":["\"Matematik Dünyası\" kanalında yayınlanan bu eğitim videosunda, bir matematik öğretmeni ikinci dereceden bir bilinmeyenli denklemler konusunu anlatmaktadır.","Video, ikinci dereceden bir bilinmeyenli denklemlerin tanımı ile başlayıp, denklemin kökleri, katsayıları ve derecesi gibi temel kavramları açıklamaktadır. Ardından çarpanlara ayırma, deneme yanılma yöntemi, çapraz çarpma, tam kareye tamamlama ve diskriminant (delta) formülü gibi farklı çözüm teknikleri örneklerle detaylı şekilde gösterilmektedir.","Öğretmen, denklemlerin çözüm kümesinin nasıl belirleneceğini, çakışık kök kavramını ve denklemlerin nasıl doğrulanacağını da açıklamaktadır. Ayrıca, reel sayılarda çözüm kümesi olmayan denklemlerin karmaşık sayılarda çözüm kümesi olabileceği de belirtilmektedir. Video boyunca öğretmen, matematikte ilerlemek için sürekli soru çözmenin önemini vurgulamaktadır."]},"endTime":2025,"title":"İkinci Dereceden Bir Bilinmeyenli Denklemler Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"İkinci Dereceden Bir Bilinmeyenli Denklemlerin Tanımı","list":{"type":"unordered","items":["İkinci dereceden bir bilinmeyenli denklemler, a·x² + b·x + c = 0 denklemidir (a, b, c reel sayılar olup a ≠ 0'dır).","Denklemde x bilinmeyen, a, b ve c katsayılar, c ise sabit terimdir.","Denklemin derecesi, x'in üstündeki en büyük sayıdır (bu örnekte 2'dir)."]},"beginTime":9,"endTime":125,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=9&ask_summarization=1"},{"index":1,"title":"Denklemin Kökü ve Çözüm Yöntemleri","list":{"type":"unordered","items":["Denklemin kökü, denklemde x yerine yazıldığında denklemin sağlandığı x değeridir.","İkinci dereceden denklemlerin iki kökü vardır ve bu kökler birbirine eşit olabilir veya farklı olabilir.","Denklemin çözümünde bilinenler bir tarafa, bilinmeyenler bir tarafa getirilir ve bilinmeyen tek başına bırakılır."]},"beginTime":125,"endTime":150,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=125&ask_summarization=1"},{"index":2,"title":"Örnek Sorular","list":{"type":"unordered","items":["x² + x + 9 = 0 denkleminin köklerinden biri -2 ise, a = 13/2 olarak bulunur.","4x² - 16 = 0 denkleminin çözüm kümesi {2, -2} olarak bulunur.","4x² + 16 = 0 denkleminin çözüm kümesi boş kümedir çünkü hiçbir sayının karesi reel sayılarda -4'e eşit değildir."]},"beginTime":150,"endTime":395,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=150&ask_summarization=1"},{"index":3,"title":"İkinci Dereceden Denklemlerin Çözümü","list":{"type":"unordered","items":["İkinci dereceden denklemlerde, benzer terimleri daire içerisine alarak ortak çarpanları bulmak önemlidir.","İki sayının çarpımı sıfır olabilmesi için her iki sayı da sıfır olmalıdır.","Çözüm kümesi, denklemi sağlayan x değerlerinin kümesidir."]},"beginTime":411,"endTime":535,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=411&ask_summarization=1"},{"index":4,"title":"Matematik Öğrenme Yöntemi","list":{"type":"unordered","items":["Matematikte ilerlemek için sürekli soru çözmek gerekir, bir veya iki soru çözerek ilerleyemeyiz.","Matematik öğretmenleri sürekli aynı şeyleri anlattıkları için bilgiler kalıcı olarak hafızada yer edinir.","Farklı tarzda sorular çözmek için deneme yanılma yöntemi kullanılabilir."]},"beginTime":535,"endTime":592,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=535&ask_summarization=1"},{"index":5,"title":"İkinci Dereceden Denklemlerin Çarpanlara Ayırılması","list":{"type":"unordered","items":["İkinci dereceden bir bilinmeyenli denklemde, x² teriminin çarpanlarını bulmak gerekir.","Çarpanların çarpımı ortadaki terimi vermelidir ve işaretleri çarpımın işaretini belirlemelidir.","Çarpanlara ayırma yöntemi, denklemi iki sayının çarpımı şeklinde yazmayı sağlar."]},"beginTime":592,"endTime":695,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=592&ask_summarization=1"},{"index":6,"title":"Çözüm Kümesinin Bulunması","list":{"type":"unordered","items":["İki sayının çarpımı sıfır olabilmesi için her iki sayı da sıfır olmalıdır.","Çözüm kümesi, denklemi sağlayan x değerlerinin kümesidir.","Aynı kökler çakışık kök olarak adlandırılır."]},"beginTime":695,"endTime":732,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=695&ask_summarization=1"},{"index":7,"title":"Farklı İkinci Dereceden Denklemler","list":{"type":"unordered","items":["İkinci dereceden denklemlerde, x² teriminin çarpanlarını bulmak için deneme yanılma yöntemi kullanılabilir.","Çarpanların çarpımı ortadaki terimi vermelidir ve işaretleri çarpımın işaretini belirlemelidir.","Çözüm kümesi, denklemi sağlayan x değerlerinin kümesidir."]},"beginTime":732,"endTime":934,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=732&ask_summarization=1"},{"index":8,"title":"Denklem Çözümü ve İşaretler","list":{"type":"unordered","items":["Denklemlerde işaretlerin doğru kullanılması önemlidir, eksi ile eksi çarpıldığında artı sonuç elde edilir.","İki sayının çarpımı sıfır ise, içlerinden birinin kesinlikle sıfır olması gerekir.","Denklemlerin çözüm kümesi, denklemin sağ tarafındaki değeri sağlayan x değerleridir."]},"beginTime":937,"endTime":1054,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=937&ask_summarization=1"},{"index":9,"title":"Kareköklü Denklemler","list":{"type":"unordered","items":["Kareköklü denklemlerde, karekök içindeki sayı çift sayı ise mutlak değer dışarı çıkarılır.","Karekök içindeki sayı pozitif veya negatif olabilir, bu nedenle çözüm kümesi iki farklı değer içerir.","Karekök içindeki sayı karesi alındığında, orijinal sayıya eşittir."]},"beginTime":1054,"endTime":1129,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=1054&ask_summarization=1"},{"index":10,"title":"Tam Kareye Tamamlama Yöntemi","list":{"type":"unordered","items":["Tam kareye tamamlama yöntemi, denklemleri iki sayının çarpımı şeklinde yazmayı amaçlar.","Denklemde eksik olan terim, denklemin her iki tarafına aynı değer eklenerek tamamlanabilir.","İki kare farkı formülü (a² - b² = (a-b)(a+b)) kullanılarak denklemler çözülebilir."]},"beginTime":1129,"endTime":1442,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=1129&ask_summarization=1"},{"index":11,"title":"Diskriminant Yöntemi","list":{"type":"unordered","items":["ax² + bx + c = 0 denklemlerinin genel çözümü için diskriminant formülü kullanılır.","Diskriminant (Δ) formülü: Δ = b² - 4ac'tir.","Denklemin kökleri: x₁ = (-b - √Δ) / 2a ve x₂ = (-b + √Δ) / 2a formülleriyle bulunur."]},"beginTime":1442,"endTime":1545,"href":"/video/preview/1130392608741864006?parent-reqid=1769794531396343-15256438397745464322-balancer-l7leveler-kubr-yp-klg-37-BAL&text=sp+classes+mathematics&t=1442&ask_summarization=1"},{"index":12,"title":"İkinci Dereceden Denklemlerin Çözümü","list":{"type":"unordered","items":["İkinci dereceden denklemlerde x²'nin önündeki katsayı a, x'in önündeki katsayı b, sabit sayı ise c olarak adlandırılır.","Diskriminant (delta) formülü b² - 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