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Консультация № 177393
21.03.2010, 16:16
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Уважаемы эксперты,помогите Отделить корни м.Штурма x4-3x3+8x2-5=0.
помогите разделить полином x4-3x3+8x2-5 на полином 4х3-9х2+16.
помогите разделить полином x4-3x3+8x2-5 на полином 4х3-9х2+16.
Обсуждение
26.03.2010, 12:43
общий
это ответ
Здравствуйте, Ушкевич Роман.
Сам метод Штурма - см.
ru.wikipedia.org/wiki/Ряд_Штурма
Деление многочленов - тоже в Яндексе можно найти.
Ряд Штурма получается таким:
f0=x^4-3x^3+8x^2-5
f1=4x^3-9x^2+16x
f2=(-37/16)x^2+2
f3=(-720/37)x+(288/37)
f4=-163/100
Далее составляем таблицу, где по горизонтали - вот эти члены ряда, а по вертикали - числа на оси х. Ячейки таблицы - знак члена ряда для этого числа, последняя строка - число смен знака у членов ряда для данного числа. Для моих чисел получилось так:
-inf. -4 -2 0 2 +inf
+ + + - + +
- - - 0 + +
- - - + - -
+ + + + - -
- - - - - -
3 3 3 2 1 1
Значит, на промежутке (-inf. +inf) = 3-1 = 2 корня
(-2; 2) = 3-1 = 2корня
(-2; 0) = 3-2 = 1корень
(0; 2) = 2-1 = 1корень
Сам метод Штурма - см.
ru.wikipedia.org/wiki/Ряд_Штурма
Деление многочленов - тоже в Яндексе можно найти.
Ряд Штурма получается таким:
f0=x^4-3x^3+8x^2-5
f1=4x^3-9x^2+16x
f2=(-37/16)x^2+2
f3=(-720/37)x+(288/37)
f4=-163/100
Далее составляем таблицу, где по горизонтали - вот эти члены ряда, а по вертикали - числа на оси х. Ячейки таблицы - знак члена ряда для этого числа, последняя строка - число смен знака у членов ряда для данного числа. Для моих чисел получилось так:
-inf. -4 -2 0 2 +inf
+ + + - + +
- - - 0 + +
- - - + - -
+ + + + - -
- - - - - -
3 3 3 2 1 1
Значит, на промежутке (-inf. +inf) = 3-1 = 2 корня
(-2; 2) = 3-1 = 2корня
(-2; 0) = 3-2 = 1корень
(0; 2) = 2-1 = 1корень
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