Maîtrisez l'Algèbre : Quiz sur les Équations et Inéquations

Question 1 sur 10 10:00

[{"id":43656,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 7","option_c":"x = 2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 2x des deux côtés et en ajoutant 7, on obtient x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43657,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La solution est x \u003E 2, donc l'affirmation est fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43658,"question":"Quel est le discriminant de l'équation x² - 5x + 6 = 0 ?","option_a":"Δ = 1","option_b":"Δ = 25","option_c":"Δ = 16","option_d":"Δ = 1","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le discriminant est calculé par Δ = b² - 4ac = 25 - 24 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43659,"question":"La factorisation de x² - 9 est :","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 : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43660,"question":"L'équation x² + 4x + 4 = 0 admet :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation se factorise en (x + 2)² = 0, donc elle admet une solution double x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43661,"question":"Quelle est la solution de l'inéquation -2x + 8 ≤ 0 ?","option_a":"x ≤ 4","option_b":"x ≥ 4","option_c":"x ≤ -4","option_d":"x ≥ -4","option_e":"","option_f":"","bonne_reponse":"B","explication":"En isolant x, on obtient x ≥ 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43662,"question":"La forme canonique de x² + 6x + 5 est :","option_a":"(x + 3)² - 4","option_b":"(x + 6)² - 31","option_c":"(x + 5)² - 20","option_d":"(x + 2)² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique est obtenue par (x + 3)² - 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43663,"question":"L'inéquation 3x + 2 \u003E 5x - 4 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La solution est x \u003C 3, donc l'affirmation est fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43664,"question":"Quel est le résultat de (x + 2)(x - 3) ?","option_a":"x² - x - 6","option_b":"x² + x - 6","option_c":"x² - 6x + 6","option_d":"x² - 5x - 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le développement donne x² - x - 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43665,"question":"L'équation 4x² - 12x + 9 = 0 admet :","option_a":"Deux solutions distinctes","option_b":"Une solution double","option_c":"Aucune solution","option_d":"Trois solutions","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant est nul, donc une solution double x = 1.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]