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Задать вопрос экспертам

Консультация № 178737

29.05.2010, 21:16

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Образование

Уважаемые эксперты, помогите пожалуйста решить задачу.
Тема: комплексные числа.
Составьте многочлен наименьшей степени с действительными коэффициентами, конями которого являются числа z₁=3i, z₂=3, z₃=-2-i.

Обсуждение

Неизвестный

29.05.2010, 21:51

общий

это ответ

Здравствуйте, STASSY.

Многочлен с действительными коэффициентами имеет комплексные корни только парные (сопряженные).
Т.к. z₁ и z₃ не являются сопряженными, то минимальная степень многочлена будет равна 5.
p(z)=(z-3*i)*(z+3*i)*(z+2+i)*(z+2-i)*(z-3)=(z²+9)*(z²+4*z+5)*(z-3)=z⁵+z⁴+2*z³-6*z²-63*z-135

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