Quiz d'algèbre : Équations, inéquations et polynômes

Question 1 sur 10 10:00

[{"id":19078,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = -12","option_c":"x = 2","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 2x = 7 + 5 → x = 12. Il s'agit d'une équation linéaire simple à résoudre.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19079,"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":"A","explication":"2x \u003E 4 → x \u003E 2. L'inégalité est bien strictement supérieure à 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19080,"question":"Quel est le développement de (x + 3)(x - 2) ?","option_a":"x² + x - 6","option_b":"x² + 5x - 6","option_c":"x² - 6","option_d":"x² + x + 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Utilisez la formule (a + b)(c + d) = ac + ad + bc + bd → x² - 2x + 3x - 6 = x² + x - 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19081,"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":"Il s'agit d'une différence de carrés : a² - b² = (a - b)(a + b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19082,"question":"L'équation x² + 4x + 4 = 0 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est nul (Δ = 0), donc une solution double : x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19083,"question":"Quelle est la solution de l'inéquation -3x + 1 ≤ 10 ?","option_a":"x ≥ -3","option_b":"x ≤ -3","option_c":"x ≥ 3","option_d":"x ≤ 3","option_e":"","option_f":"","bonne_reponse":"B","explication":"-3x ≤ 9 → x ≥ -3 (attention au changement de sens de l'inégalité car on divise par un nombre négatif).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19084,"question":"Le polynôme x³ - 8 peut s'écrire sous la forme :","option_a":"(x - 2)(x² + 2x + 4)","option_b":"(x + 2)(x² - 2x + 4)","option_c":"(x - 2)³","option_d":"(x + 2)³","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il s'agit d'une différence de cubes : a³ - b³ = (a - b)(a² + ab + b²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19085,"question":"L'équation 2x² - 5x + 2 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 25 - 16 = 9 \u003E 0, donc deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19086,"question":"Quelle est la valeur de x pour laquelle le polynôme x² - 6x + 9 est nul ?","option_a":"x = 3","option_b":"x = -3","option_c":"x = 9","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le polynôme est un carré parfait : (x - 3)² = 0 → x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19087,"question":"La solution de l'équation 4x + 1 = 2(2x - 3) est :","option_a":"x = -7\/2","option_b":"x = 7\/2","option_c":"x = -1","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"4x + 1 = 4x - 6 → 1 = -6, ce qui est impossible. Donc pas de solution.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]