Maîtrisez l'algèbre : Équations, polynômes et inéquations

Question 1 sur 10 10:00

[{"id":40545,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 15","option_d":"x = 5\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'équation en isolant x : 3x = 15 → x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40546,"question":"L'équation x² - 4x + 4 = 0 admet deux solutions distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 0, donc l'équation admet une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40547,"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":"Utilisez l'identité remarquable a² - b² = (a - b)(a + b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40548,"question":"La solution de l'inéquation 2x + 1 \u003E 5 est :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'inéquation : 2x \u003E 4 → x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40549,"question":"Le polynôme P(x) = x³ - 2x² + x est divisible par x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"P(0) = 0, donc x est un facteur de P(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40550,"question":"Quelle est la somme des racines de l'équation x² - 5x + 6 = 0 ?","option_a":"5","option_b":"6","option_c":"-5","option_d":"-6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une équation ax² + bx + c = 0, la somme des racines est -b\/a.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40551,"question":"La fraction (x² - 4)\/(x - 2) est simplifiable pour x ≠ 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Factorisez le numérateur : (x - 2)(x + 2)\/(x - 2) = x + 2 (pour x ≠ 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40552,"question":"Quelle est la solution de l'équation |2x - 1| = 3 ?","option_a":"x = 2 ou x = -1","option_b":"x = 2 ou x = 1","option_c":"x = -2 ou x = 1","option_d":"x = -2 ou x = -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez |2x - 1| = 3 → 2x - 1 = 3 ou 2x - 1 = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40553,"question":"Le polynôme Q(x) = x⁴ - 16 peut s'écrire sous la forme (x² - 4)(x² + 4).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Factorisez avec l'identité a² - b² : (x²)² - 4² = (x² - 4)(x² + 4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40554,"question":"Quelle est la solution de l'inéquation x² - 3x - 4 ≤ 0 ?","option_a":"x ∈ [-1, 4]","option_b":"x ∈ ]-∞, -1] ∪ [4, +∞[","option_c":"x ∈ [1, 4]","option_d":"x ∈ ]-∞, 1] ∪ [4, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'inéquation en trouvant les racines (x = -1 et x = 4) et en étudiant le signe du polynôme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]