Algèbre 3ème secondaire : Équations, inéquations et polynômes

Question 1 sur 10 10:00

[{"id":66632,"question":"Quelle est la solution de l'équation 2x - 5 = 3x + 1 ?","option_a":"x = -6","option_b":"x = -4","option_c":"x = 4","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'équation : 2x - 5 = 3x + 1 → -5 - 1 = 3x - 2x → x = -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66633,"question":"L'inéquation 3x + 2 ≤ 5x - 4 a pour solution x ≥ 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvez l'inéquation : 3x + 2 ≤ 5x - 4 → 2 + 4 ≤ 5x - 3x → 6 ≤ 2x → x ≥ 3. L'affirmation est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66634,"question":"Quel est le degré du polynôme P(x) = 4x³ - 2x² + x - 7 ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le degré d'un polynôme est le plus haut exposant de x. Ici, c'est 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66635,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum en x = 2 ?","option_a":"Oui, car f(2) = -1","option_b":"Non, car elle n'a pas de minimum","option_c":"Oui, car la dérivée s'annule en x = 2","option_d":"Non, car f(2) = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2. f(2) = -1, qui est le minimum de la fonction.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66636,"question":"L'équation x² - 5x + 6 = 0 a pour solutions x = 2 et x = 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Factorisez : (x - 2)(x - 3) = 0 → x = 2 ou x = 3. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66637,"question":"Quel est le résultat de la division de P(x) = x³ - 2x² + x - 1 par (x - 1) ?","option_a":"x² - x + 2","option_b":"x² - x - 1","option_c":"x² + x - 1","option_d":"x² - 2x + 1","option_e":"","option_f":"","bonne_reponse":"D","explication":"Effectuez la division polynomiale ou utilisez le schéma de Horner : le quotient est x² - x - 1 et le reste est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66638,"question":"L'inéquation (x - 1)(x + 2) \u003E 0 a pour solution x ∈ ]-∞, -2[ ∪ ]1, +∞[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Étudiez le signe du produit : positif lorsque x \u003C -2 ou x \u003E 1. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66639,"question":"Quelle est la forme factorisée de P(x) = x³ - 3x² + 3x - 1 ?","option_a":"(x - 1)³","option_b":"(x - 1)(x² - 2x + 1)","option_c":"(x - 1)(x² + x + 1)","option_d":"(x + 1)³","option_e":"","option_f":"","bonne_reponse":"A","explication":"Développez (x - 1)³ = x³ - 3x² + 3x - 1. La forme factorisée est donc (x - 1)³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66640,"question":"La fonction f(x) = -2x² + 4x - 1 admet-elle un maximum en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = -4x + 4 s'annule en x = 1. f(1) = 1, qui est le maximum de la fonction (coefficient de x² négatif).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66641,"question":"Résolvez l'équation 3x² - 12x + 9 = 0.","option_a":"x = 1 ou x = 3","option_b":"x = -1 ou x = 3","option_c":"x = 1 ou x = -3","option_d":"x = -1 ou x = -3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Factorisez : 3(x² - 4x + 3) = 0 → 3(x - 1)(x - 3) = 0 → x = 1 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]