Algèbre Seconde : Maîtrisez les équations et fonctions polynomiales

Question 1 sur 10 10:00

[{"id":11348,"question":"Quelle est la solution de l'équation 3x - 5 = 0 ?","option_a":"x = 5\/3","option_b":"x = -5\/3","option_c":"x = 3\/5","option_d":"x = -3\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 0, on isole x : 3x = 5, donc x = 5\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11349,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, donc l'équation admet une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11350,"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 : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11351,"question":"L'inéquation 2x + 1 \u003E 5 a pour solution x \u003E 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x + 1 \u003E 5, on obtient 2x \u003E 4, donc x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11352,"question":"Quel est le degré du polynôme 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 la plus haute puissance de x, ici 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11353,"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":"Cette fonction est un polynôme du second degré qui s'annule en x = 1 et x = 3, donc elle n'est pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11354,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"x ∈ [2 ; 3]","option_b":"x ∈ ]-∞ ; 2] ∪ [3 ; +∞[","option_c":"x ∈ [1 ; 6]","option_d":"x ∈ ]-∞ ; 1] ∪ [6 ; +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le polynôme x² - 5x + 6 se factorise en (x - 2)(x - 3), donc il est négatif ou nul entre 2 et 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11355,"question":"Le discriminant d'une équation du second degré 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 coefficients de l'équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11356,"question":"Quelle est la représentation graphique d'une fonction affine ?","option_a":"Une droite","option_b":"Une parabole","option_c":"Un cercle","option_d":"Une hyperbole","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine f(x) = ax + b a pour représentation graphique une droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11357,"question":"Si f(x) = 2x² - 8x + 5, quelle est la valeur de f(2) ?","option_a":"-3","option_b":"5","option_c":"-7","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x par 2 dans f(x), on obtient f(2) = 2*(2)² - 8*2 + 5 = 8 - 16 + 5 = -3. (Note : correction de l'option correcte à -3)","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]