Gönderen Konu: polinomun gerçek kökleri yoktur {solved} (Okunma sayısı 3410 defa)

stuart clark · « : Mayıs 27, 2011, 06:19:51 öö »

find the condition for which the equation $\mathbf{x^n+a_{1}x^{n-1}+a_{2}x^{n-2}+............+a_{n}=0}$$ can not have real roots.

options:

(1) $\mathbf{(n-1)a_{1}^2-2n.a_{2}>0}$

(2) $\mathbf{(n-1)a_{1}^2-2n.a_{2}<0}$

(3) $\mathbf{n.a_{1}^2-2(n-1)a_{2}<0}$

(4) None of these.

Lokman Gökçe · « **Yanıtla #1 :** 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.

stuart clark · « **Yanıtla #2 :** Mayıs 28, 2011, 04:05:21 öö »

thanks scarface.

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Gönderen Konu: polinomun gerçek kökleri yoktur {solved} (Okunma sayısı 3410 defa)

stuart clark

polinomun gerçek kökleri yoktur {solved}

Lokman Gökçe

Ynt: polinomun gerçek kökleri yoktur {solved}

stuart clark

Ynt: polinomun gerçek kökleri yoktur {solved}