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Консультация № 189071
03.04.2016, 14:13
0.00 руб.
03.04.2016, 14:20
0
3
1
Здравствуйте! У меня возникли сложности с таким вопросом:
помогите найти рациональные корни:
2*x^(4)+17*x^(3)+2*x^(2)-9*x-3
помогите найти рациональные корни:
2*x^(4)+17*x^(3)+2*x^(2)-9*x-3
Обсуждение
03.04.2016, 14:21
общий
Обратите, пожалуйста, внимание на эту консультацию, перенесённую из другого раздела.
Об авторе:
Facta loquuntur.
Facta loquuntur.
03.04.2016, 14:26
общий
Адресаты:
Воспользуйтесь утверждением: "Числитель ненулевого рационального корня многочлена с действительными коэффициентами является делителем свободного члена, а знаменатель - делителем старшего коэффициента".
Об авторе:
Facta loquuntur.
Facta loquuntur.
03.04.2016, 16:59
общий
это ответ
Здравствуйте, bill1091989!
Пусть дан многочлен
Старший коэффициент этого многочлена
а свободный член 
Воспользуемся утверждением: "Числитель ненулевого рационального корня многочлена с действительными коэффициентами является делителем свободного члена, а знаменатель - делителем старшего коэффициента". Согласно этому утверждению, рациональными корнями заданного многочлена могут быть лишь числа
Подставляя эти числа в многочлен, получим
Следовательно, многочлен имеет один лишь рациональный корень
С уважением.
Пусть дан многочлен
Старший коэффициент этого многочлена
а свободный член Воспользуемся утверждением: "Числитель ненулевого рационального корня многочлена с действительными коэффициентами является делителем свободного члена, а знаменатель - делителем старшего коэффициента". Согласно этому утверждению, рациональными корнями заданного многочлена могут быть лишь числа
Подставляя эти числа в многочлен, получим
Следовательно, многочлен имеет один лишь рациональный корень
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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