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Консультация № 189779
17.09.2016, 20:06
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос ( № 10 ):
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Обсуждение
17.09.2016, 22:55
общий
это ответ
Здравствуйте, anton74551!
По-моему, теорему можно доказать методом от противного.
Предположим, что квадратный трёхчлен
не имеет корней, но его можно представить в виде произведения двух линейных множителей, то есть
Если
или 
то правая часть уравнения 
при 
становится равной нулю. Тогда числа 
или 
являются корнями квадратного трёхчлена 
который по условию теоремы не имеет корней. Получили противоречие, которое свидетельствует о неверности принятого предположения. Значит, теорема верна.
По-моему, теорему можно доказать методом от противного.
Предположим, что квадратный трёхчлен
не имеет корней, но его можно представить в виде произведения двух линейных множителей, то естьЕсли
или то правая часть уравнения при становится равной нулю. Тогда числа или являются корнями квадратного трёхчлена который по условию теоремы не имеет корней. Получили противоречие, которое свидетельствует о неверности принятого предположения. Значит, теорема верна.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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