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Sınıf Anka Yayınları Matematik Kitabı İkinci Dereceden Denklemler Alıştırmaları Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"İkinci Dereceden Denklemlerin Kökleri","list":{"type":"unordered","items":["Sınıf Anka Yayınları matematik kitabının 203 ve 204 sayfalarındaki alıştırma çözümleri yapılacak.","İkinci derecede bir bilinmeyenli denklemlerin genel formülü ax² + bx + c = 0'dır.","Kökler toplamı -b/a, kökler çarpımı c/a formülleri kullanılarak denklemlerde boş yerler doldurulacak."]},"beginTime":0,"endTime":58,"href":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=0&ask_summarization=1"},{"index":1,"title":"İlk Alıştırmanın Çözümü","list":{"type":"unordered","items":["İlk denklemde a=4, b=3, c=-2 olduğunda kökler toplamı -3/4, kökler çarpımı -1/2 olarak hesaplanır.","İkinci denklemde a=-1, b=5, c=-1 olduğunda kökler toplamı 5, kökler çarpımı 1 olarak bulunur.","Üçüncü denklemde a=2, b=7, c=-3 olduğunda kökler toplamı -5/2, kökler çarpımı -3/2 olarak hesaplanır.","Dördüncü denklemde a=1, b=-6, c=9 olduğunda kökler toplamı 6, kökler çarpımı 9 olarak bulunur."]},"beginTime":58,"endTime":190,"href":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=58&ask_summarization=1"},{"index":2,"title":"İkinci Alıştırmanın Çözümü","list":{"type":"unordered","items":["İkinci alıştırmada kökleri x₁ ve x₂ olan denklemler için istenen değerler bulunacak.","x₁ + x₂ = -b/a formülü kullanılarak kökler toplamı hesaplanır.","x₁ × x₂ = c/a formülü kullanılarak kökler çarpımı bulunur.","Kökler toplamı ve çarpımı ile ilgili karmaşık ifadeler sadeleştirilerek çözülür."]},"beginTime":190,"endTime":598,"href":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=190&ask_summarization=1"},{"index":3,"title":"Üçüncü Alıştırmanın Çözümü","list":{"type":"unordered","items":["Üçüncü alıştırmada kökleri verilen ikinci dereceden denklemler bulunacak.","İkinci dereceden denklemlerin genel formülü ax² + bx + c = 0'dan yola çıkılarak çözüm yapılır.","Kökler toplamı ve çarpımı kullanılarak denklem yazılır: x² - (kökler toplamı)x + (kökler çarpımı) = 0, örneğin kökleri 8 ve 3 olan denklem x² - 11x + 24 = 0 olarak bulunur."]},"beginTime":598,"endTime":735,"href":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=598&ask_summarization=1"},{"index":4,"title":"İkinci Dereceden Denklemlerin Kökleri","list":{"type":"unordered","items":["İkinci dereceden denklemlerde kökler toplamı ve çarpımı formülleri kullanılarak denklemler yazılabilir.","Kökler toplamı formülü: -b/a, kökler çarpımı formülü: c/a'dır.","Denklemlerde paydalardan kurtulmak için her iki tarafı aynı sayı ile çarpma veya paydaları eşitleme yöntemleri kullanılabilir."]},"beginTime":747,"endTime":848,"href":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=747&ask_summarization=1"},{"index":5,"title":"Kökler Verilmiş Denklemlerin Çözümü","list":{"type":"unordered","items":["Kökler verilmiş ikinci dereceden denklemlerde, kökler toplamı ve çarpımı formülleri kullanılarak denklem yazılabilir.","Kökler toplamı ve çarpımı formülleri: x² - (kökler toplamı)x + (kökler çarpımı) = 0 denkleminde yerine yazılır.","Kökler toplamı ve çarpımı formülleri kullanılarak x² - 2x - 1 = 0, x² - 2x - 70 = 0, x² + 8/3x - 1 = 0 denklemleri elde edilir."]},"beginTime":848,"endTime":1329,"href":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=848&ask_summarization=1"},{"index":6,"title":"Köklerin Değiştirilmesi","list":{"type":"unordered","items":["Köklerin değiştirilmesi durumunda, kökler toplamı ve çarpımı formülleri kullanılarak yeni denklem yazılabilir.","Köklerden birine 2 eklenildiğinde, kökler toplamı 15/3, kökler çarpımı 25/3 olur ve denklem x² - 20x + 25 = 0 denklemine dönüşür.","Köklerden birine 3 çarpılıp 1 eklenildiğinde, kökler toplamı 0, kökler çarpımı 0, denklem x² = 0 denklemine dönüşür."]},"beginTime":1329,"endTime":1469,"href":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=1329&ask_summarization=1"},{"index":7,"title":"İkinci Dereceden Denklemler Alıştırmaları","list":{"type":"unordered","items":["Köklerin toplamı ve çarpımı kullanılarak ikinci dereceden bir bilinmeyenli denklem oluşturulabilir.","Köklerin aritmetik ortalaması (x₁ + x₂) ve geometrik ortalaması (√(x₁ × x₂)) eşit olduğunda, denklemin çözümü bulunabilir.","Kökler toplamı (-b/a) ve kökler çarpımı (c/a) formülleri kullanılarak denklemin katsayıları hesaplanabilir."]},"beginTime":1475,"endTime":1600,"href":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=1475&ask_summarization=1"},{"index":8,"title":"Köklerle İlgili Alıştırmalar","list":{"type":"unordered","items":["Köklerin belirli bir ifadesinin değeri, kökler toplamı ve çarpımı formülleri kullanılarak hesaplanabilir.","Kökler toplamı ve çarpımı eşit olduğunda, denklemin katsayıları arasındaki ilişki bulunabilir.","Köklerin belirli bir değerinin çarpımı, köklerin toplamı ve çarpımı formülleri kullanılarak hesaplanabilir."]},"beginTime":1600,"endTime":2012,"href":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=1600&ask_summarization=1"},{"index":9,"title":"Köklerle İlgili Karmaşık Alıştırmalar","list":{"type":"unordered","items":["Kökler çarpımı verildiğinde, denklemin katsayıları arasındaki ilişki kullanılarak bilinmeyen bulunabilir.","Kökler arasında belirli bir ilişki olduğunda, kökler çarpımı formülü kullanılarak bilinmeyen bulunabilir.","203 ve 204 sayfadaki alıştırmaların çözümleri tamamlanmıştır."]},"beginTime":2012,"endTime":2159,"href":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=2012&ask_summarization=1"}],"linkTemplate":"/video/preview/14874779180415379019?parent-reqid=1769672125837775-5622873891657157185-balancer-l7leveler-kubr-yp-sas-85-BAL&text=anktry203&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"10 Sınıf Anka Yayınları Matematik Alıştırmalar sayfa 203 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