Geomania.Org Forumları

Fantezi Cebir => Analiz-Cebir => Konuyu başlatan: stuart clark - Mayıs 28, 2011, 04:09:01 öö

Başlık: maksimum gerçek çözüm {solved}
Gönderen: stuart clark - Mayıs 28, 2011, 04:09:01 öö

maximum number of real solution of the equation (http://latex.codecogs.com/gif.latex?\mathbf{ax^n+x^2+bx+c=0}$).where (http://latex.codecogs.com/gif.latex?\mathbf{a,b,c\in\mathbb{R},n=}$) even positive integer.

Başlık: Ynt: maksimum gerçek çözüm {solved}
Gönderen: Lokman Gökçe - Mayıs 28, 2011, 02:06:35 ös

answer is 2.

solution:

Let f(x) = axⁿ, g(x) = - x² - bx - c. We have to find the number of the real solutions of the equation f(x) = g(x). Since graphs of y = f(x), y = g(x) are intersect at most two different points, maximum number of the real solutions of the equation axⁿ + x² + bx + c = 0 is 2.