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Résoudre une équation du second degré avec la méthode du discriminant.

Soit $ax^2+bx+c=0$ une équation du second degré, à coefficients réels, alors résoudre cette équation dans IR se fait selon la méthode suivante:

1)On calcule le DISCRIMINANT: $\Delta=b^2-4ac$

2)On regarde le signe du discriminant

*si $\Delta < 0$ (strictement négatif), on peut en conclure que l'équation n'admet pas de solutions réelles

*si $\Delta=0$ , il y a deux solutions confondues, donc une seule qui est $x_1 = \frac{-b}{2a}$

*si $\Delta>0$ (strictement positif) : aller au 3

3) L'équation admet deux solutions réelles $x_1$ et $x_2$ , telles que: $x_1=\frac{-b-\sqrt{\Delta}}{2a}$ et $x_2=\frac{-b+\sqrt{\Delta}}{2a}$

4)Etape facultative: *on verifie que les solutions trouvées annulent bien le trinome $ax^2+bx+c$ *si vraiment on a un doute, on trace sur une calculatrice graphique le trinome $ax^2+bx+c$ et on regarde si les intersections éventuelles de la parabole et de l'axe des abscisses se situent au niveau de $x_1$ et $x_2$ (approximativement)

en cas d'erreur, guillaume@webmaths.com

Last update: 2005-08-06 15:17
Author: Guillaume

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Òîëüêî âîò â÷åðà îá ýòîì äóìàë, òàê ÷òî ïîñò îïðåäåëåííî â òåìó!

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Çàíèìàòåëüíàÿ è èíòåðåñíàÿ ñòàòüÿ ó âàñ. Â îòëè÷èå îò áîëüøèíñòâà äðóãèõ ïîõîæèõ ìèíèìóì âîäû! :)

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Вообще-то, многое из того, что Вы пишете не совсем так… Ну да ладно,не важно в общем :)

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Хм... что-то у меня ссылка не открывается, которую указали. Это у всех так?

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Ну так и без недостатков и достоинства не так заметны :)

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Все замечательно: и по стилю изложения, и по содержимому. Так держать!

Comment of Ñîãëàñíûå:
Люди в подобных случаях так говорят - Бей в решето, коли в сито не пошло. ;)

Comment of Áîëåçíü:
Увлекательно было почитать :) Попробуем-с тоже ответить в ближайших темах.

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Comment of Âàëåíòèí:
Занятно. Вопрос только в том, как это будет выглядеть в будущем :)

Comment of XÓËÈÃAH:
Сдается мне, на вашем блоге развелось слишком много так называемых говн*комментатров, которым лишь бы ляпнуть чего-нибудь:)

Comment of deserdca.ru:
Эээ, объясните, плиз, а то я че-то не совсем в тему въехал, это как?

Comment of Àôàíàñèé:
Большое спасибо. Давно такое искал :)

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Maths » Lycée » Analyse Résoudre une équation du second degré avec la méthode du discriminant.

Maths » Lycée » Analyse
Résoudre une équation du second degré avec la méthode du discriminant.