Quiz : Équations et Inéquations — 3ème Année Secondaire

Question 1 sur 10 10:00

[{"id":71072,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0. Les solutions sont donc x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71073,"question":"L'inéquation 2x - 3 \u003E 5 a pour solution x \u003E 4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x - 3 \u003E 5, on obtient 2x \u003E 8, soit x \u003E 4. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71074,"question":"Quelle méthode permet de résoudre une équation du second degré ?","option_a":"Méthode de la factorisation uniquement","option_b":"Méthode du discriminant uniquement","option_c":"Méthode de la factorisation ou du discriminant","option_d":"Méthode graphique uniquement","option_e":"","option_f":"","bonne_reponse":"C","explication":"Une équation du second degré peut être résolue par factorisation si elle est factorisable, ou par la méthode du discriminant (formule Δ = b² - 4ac) dans les autres cas.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71075,"question":"La solution de l'inéquation x² - 4x + 3 ≤ 0 est :","option_a":"x ∈ [1 ; 3]","option_b":"x ∈ ]-∞ ; 1] ∪ [3 ; +∞[","option_c":"x ∈ [0 ; 4]","option_d":"x ∈ ]-∞ ; 0] ∪ [4 ; +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'inéquation x² - 4x + 3 ≤ 0 se résout en trouvant les racines (x=1 et x=3) et en étudiant le signe du trinôme. La solution est l'intervalle entre les racines, soit [1 ; 3].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71076,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est toujours positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant peut être positif, nul ou négatif selon les valeurs de a, b et c. Il n'est pas toujours positif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71077,"question":"Quelle est la solution de l'équation 3(x - 2) = 2x + 1 ?","option_a":"x = 7","option_b":"x = -7","option_c":"x = 5","option_d":"x = -5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant, on obtient 3x - 6 = 2x + 1, soit x = 7. La solution est donc x = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71078,"question":"L'ensemble des solutions de l'inéquation -2x + 5 \u003E 0 est :","option_a":"x \u003C 2,5","option_b":"x \u003E 2,5","option_c":"x \u003C -2,5","option_d":"x \u003E -2,5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant -2x + 5 \u003E 0, on obtient -2x \u003E -5, soit x \u003C 2,5 (en divisant par un nombre négatif, on inverse le sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71079,"question":"Une équation du second degré admet toujours deux solutions distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une équation du second degré peut avoir deux solutions distinctes, une solution double (si Δ = 0) ou aucune solution réelle (si Δ \u003C 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71080,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés, qui se factorise en (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71081,"question":"La solution de l'équation 2x² - 8x = 0 est :","option_a":"x = 0 ou x = 4","option_b":"x = 0 ou x = -4","option_c":"x = 2 ou x = -2","option_d":"x = 1 ou x = -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En factorisant, on obtient 2x(x - 4) = 0. Les solutions sont donc x = 0 et x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]