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[{"id":75852,"question":"Quelle est la solution de l'équation 3x² - 12x + 9 = 0 ?","option_a":"x = 1 ou x = 3","option_b":"x = -1 ou x = -3","option_c":"x = 2","option_d":"Pas de solution réelle","option_e":"","option_f":"","bonne_reponse":"A","explication":"On factorise l'équation : 3(x² - 4x + 3) = 0 → 3(x-1)(x-3) = 0. Les solutions sont donc x=1 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75853,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle croissante sur l'intervalle [0, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x + 2. Sur [0,2], f'(x) change de signe (négative puis positive), donc la fonction n'est pas croissante sur tout l'intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75854,"question":"Quel est le reste de la division euclidienne de P(x) = 2x³ - 5x² + 3x - 7 par (x - 2) ?","option_a":"-5","option_b":"3","option_c":"-7","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème du reste, P(2) = 2(8) - 5(4) + 3(2) - 7 = 16 - 20 + 6 - 7 = -5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75855,"question":"L'inéquation (x+1)(x-3) \u003E 0 a pour solution :","option_a":"x ∈ ]-∞, -1[ ∪ ]3, +∞[","option_b":"x ∈ ]-1, 3[","option_c":"x ∈ ]-∞, 3[","option_d":"x ∈ ]-1, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit est positif lorsque les deux facteurs sont de même signe, soit x \u003C -1 ou x \u003E 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75856,"question":"La fonction f(x) = (2x + 1)\/(x - 3) admet-elle une asymptote verticale ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car le dénominateur s'annule en x=3, ce qui crée une asymptote verticale en cette valeur.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75857,"question":"Quel est le coefficient dominant du polynôme P(x) = 4x⁴ - 3x³ + 2x - 5 ?","option_a":"4","option_b":"-3","option_c":"2","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient dominant est le coefficient du terme de plus haut degré, ici 4x⁴.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75858,"question":"L'équation x⁴ - 5x² + 4 = 0 admet pour solutions :","option_a":"x = ±1 ou x = ±2","option_b":"x = ±√5","option_c":"x = 0 ou x = ±√5","option_d":"Pas de solution réelle","option_e":"","option_f":"","bonne_reponse":"A","explication":"On pose y = x² : y² - 5y + 4 = 0 → (y-1)(y-4)=0 → y=1 ou y=4 → x=±1 ou x=±2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75859,"question":"La fonction f(x) = x² - 4x + 3 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Non, car son discriminant est positif (Δ=4) et elle s'annule en x=1 et x=3. Elle est donc négative entre ces racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75860,"question":"Quel est le degré du polynôme P(x) = (x² + 1)(x³ - 2x + 5) ?","option_a":"5","option_b":"6","option_c":"3","option_d":"2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le degré d'un produit de polynômes est la somme des degrés : 2 + 3 = 5. Le terme dominant est x² * x³ = x⁵.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75861,"question":"L'inégalité |2x - 5| ≤ 3 a pour solution :","option_a":"x ∈ [1, 4]","option_b":"x ∈ [-3, 3]","option_c":"x ∈ ]-∞, 1] ∪ [4, +∞[","option_d":"x ∈ [0, 5]","option_e":"","option_f":"","bonne_reponse":"A","explication":"On résout -3 ≤ 2x-5 ≤ 3 → 2 ≤ 2x ≤ 8 → 1 ≤ x ≤ 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]