Les trinômes du second degré : Factorisation, équations et applications

Question 1 sur 10 10:00

[{"id":4749,"question":"Quelle est la forme générale d'un trinôme du second degré ?","option_a":"ax + b","option_b":"ax² + bx + c","option_c":"a\/x + b","option_d":"a(x + b)² + c","option_e":"","option_f":"","bonne_reponse":"B","explication":"La forme générale d'un trinôme du second degré est bien ax² + bx + c, où a, b et c sont des coefficients réels et a ≠ 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4750,"question":"Le trinôme x² - 5x + 6 peut-il se factoriser ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai, car on peut l'écrire sous la forme (x - 2)(x - 3), ce qui donne les racines x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4751,"question":"Quel est le discriminant du trinôme 2x² - 4x + 1 ?","option_a":"Δ = 8","option_b":"Δ = 4","option_c":"Δ = 6","option_d":"Δ = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant se calcule par Δ = b² - 4ac = (-4)² - 4*2*1 = 16 - 8 = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4752,"question":"Si Δ \u003C 0 pour une équation du second degré, combien de solutions réelles a-t-elle ?","option_a":"0 solution","option_b":"1 solution","option_c":"2 solutions","option_d":"Une infinité de solutions","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si Δ \u003C 0, l'équation n'a pas de solution réelle (les solutions sont complexes).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4753,"question":"La factorisation x² - 9 est égale à :","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":"On reconnaît une identité remarquable : x² - 9 = x² - 3² = (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4754,"question":"Le trinôme 3x² + 6x + 3 a pour discriminant Δ = 0. Que peut-on en déduire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai, car Δ = 6² - 4*3*3 = 36 - 36 = 0, ce qui signifie qu'il y a une racine double.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4755,"question":"Résoudre l'équation x² + 4x - 5 = 0.","option_a":"x = 1 ou x = -5","option_b":"x = -1 ou x = 5","option_c":"x = 2 ou x = -3","option_d":"x = -2 ou x = 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions sont x = 1 et x = -5, obtenues en factorisant (x + 5)(x - 1) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4756,"question":"Le sommet de la parabole associée à f(x) = x² - 4x + 3 a pour abscisse :","option_a":"x = 2","option_b":"x = -2","option_c":"x = 1","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'abscisse du sommet est donnée par x = -b\/(2a) = 4\/2 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4757,"question":"Un trinôme du second degré peut-il avoir une seule racine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai, lorsque le discriminant est égal à 0, le trinôme a une racine double (une seule racine réelle).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4758,"question":"Quelle est la valeur de c dans le trinôme 4x² + 8x + c si son discriminant est Δ = 0 ?","option_a":"c = 4","option_b":"c = 8","option_c":"c = 16","option_d":"c = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si Δ = 0, alors b² - 4ac = 0 → 8² - 4*4*c = 0 → 64 = 16c → c = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]