22.Определение многочлена. Сложение, умножение на число и перемножение многочленов. Алгоритм Евклида деления многочлена на многочлен, целая часть, дробная часть и остаток от деления. Теорема Безу. Корни многочлена и их кратность. Основная теорема алгебры многочленов. Разложение многочлена на множители.
Многочлен-это сумма одночленов.
Сложение и вычитание многочленов:
-составить их сумму и разность соответственно;
-раскрыть скобки, прийти к многочлену,
-полученный многочлен привести к стандартному виду.
Для умножения многочлена на многочлен: необходимо каждый член одного многочлена умножить на каждый член другого многочлена и найти сумму полученных произведений.
f(x) , g(x) принадлежат P[x] ; g(x)не равно 0. Тогда можно разделить с остатком f(x) на g(x).
f(x)=g(x)q(x)+r(x) , если r(x) 0, степень r(x)<степени g(x).
Разделим g(x) на r(x) с остатком g(x)=r(x)q1(x)+r1(x), если r1(x)не равно0 степень r1 < степени r.
Разделим r(x) на r1(x) и т.д.
Так как степени остатков все время убывают, то на каком-то шаге остаток rk+1(x)=0.
f(x)=g(x)q(x)+r(x) ; r(x)не равно 0
g(x)=r(x)q1(x)+r1(x) ; r1(x) не равно 0 ; cт. r1 < ст. r
(4) r(x)=r1(x)q2(x)+r2(x)
rk-1(x)=rk(x)qk+1(x)+rk+1(x), rk+1(x)=0.
Процесс последовательного получения равенств (4) называют алгоритмом Евклида для многочленов f(x) и g(x). Последний отличный от нуля остаток — rk.
Т.Безу Остаток от деления многочлена P(x) на двучлен (x−a) равен P(a) .
Следствия из теоремы Безу:
Число a - корень многочлена P(x) тогда и только тогда, когда P(x) делится без остатка на двучлен x−a .
Отсюда, в частности, следует, что множество корней многочлена P(x) тождественно множеству корней соответствующего уравнения P(x)=0 .
Свободный член многочлена делится на любой целый корень многочлена с целыми коэффициентами (если старший коэффициент равен 1, то все рациональные корни являются и целыми).
Пусть a - целый корень приведенного многочлена P(x) с целыми коэффициентами. Тогда для любого целого k число P(k) делится на a−k .
| 21.Определение комплексных чисел, действия над ними. Тригонометрическая и показательная формы для записи чисел. Возведение в целую степень и извлечение корня. Формула Муавра.
Комплексными числами называют пары (x,y) вещественных (действительных) чисел x и y, для которых следующим образом определены понятие равенства и операции сложения и умножения. Обозначим комплексное число (x,y) буквой z, то есть положим z=(x,y). Пусть z1=(x1,y1), z2=(x2,y2). Два комплексных числа z1 и z2 считаются равными тогда и только тогда, когда x1=x2 и y1=y2, то есть {(x1,y1)=(x2,y2)}⇔{x1=x2} ∧ {y1=y2}
Запись комплексного числа z=(x,y)z=(x,y) в виде z=x+iy называют алгебраической формой комплексного числа.
Если x=0, то есть z=iy, то такое комплексное число называют чисто мнимым.
Здесь и всюду в дальнейшем, если не оговорено противное, в записи x+iy числа x и y считаются действительными (вещественными).
Число sqrt(x^2+y^2) обозначают |z| и называют модулем комплексного числа z, то есть |z|=|x+iy|= sqrt(x^2+y^2)
Операции сложения и умножения комплексных чисел обладают свойствами:
Коммутативности z1+z2=z2+z1, z1z2=z2z1;
ассоциативности,(z1+z2)+z3=z1+(z2+z3),(z1z2)z3=z1(z2z3);
дистрибутивности z1(z2+z3)=z1z2+z1z3.
Формула Муавра:
![](data:image/png;base64,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)
Тригонометрическая форма комплексного числа:
Для всякого комплексного числа z=x+iy справедливо равенство z=|z|(cosφ+isinφ).
![](data:image/png;base64,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)
| 20.Поверхности второго порядка: Эллипсоид, гиперболлоид и т д
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)
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