Geomania.Org Forumları

Fantezi Cebir => Analiz-Cebir => Konuyu başlatan: stuart clark - Mayıs 27, 2011, 06:19:51 öö

Başlık: polinomun gerçek kökleri yoktur {solved}
Gönderen: stuart clark - Mayıs 27, 2011, 06:19:51 öö

find the condition for which the equation (http://latex.codecogs.com/gif.latex?\mathbf{x^n+a_{1}x^{n-1}+a_{2}x^{n-2}+............+a_{n}=0}$) can not have real roots.

options:

(1) (http://latex.codecogs.com/gif.latex?\mathbf{(n-1)a_{1}^2-2n.a_{2}%3E0})

(2) (http://latex.codecogs.com/gif.latex?\mathbf{(n-1)a_{1}^2-2n.a_{2}%3C0})

(3) (http://latex.codecogs.com/gif.latex?\mathbf{n.a_{1}^2-2(n-1)a_{2}%3C0})

(4) None of these.

Başlık: Ynt: polinomun gerçek kökleri yoktur {solved}
Gönderen: Lokman Gökçe - Mayıs 27, 2011, 09:52:54 öö

Inrermediate Value Theorem: If f(x) is a continious function on interval [a, b] and f(a).f(b) < 0 then the equation f(x) = 0 have at least one real root in interval (a, b).

According to the inrermediate value theorem:

If a_n < 0 and n is an odd number, then the given polynomial have at least one real root in interval (- ∞, ∞).

If a_n < 0 and n is an even number, then the given polynomial have at least one real root in interval (0, ∞).

Furthermore, conditions (1), (2), (3) are incompetent pooryl. Correct option is (4): None of these.

Başlık: Ynt: polinomun gerçek kökleri yoktur {solved}
Gönderen: stuart clark - Mayıs 28, 2011, 04:05:21 öö

thanks scarface.