Les trinômes du second degré : Factorisation, Équations et Discriminant

Question 1 sur 10 10:00

[{"id":4932,"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 - α)(x - β)","option_d":"x² + y²","option_e":"","option_f":"","bonne_reponse":"B","explication":"Un trinôme du second degré s'écrit sous la forme ax² + bx + c, où a, b et c sont des réels et a ≠ 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4933,"question":"Le discriminant d'un trinôme permet de déterminer :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac permet de déterminer la nature des racines (réelles, complexes ou doubles) d'une équation quadratique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4934,"question":"Si Δ \u003E 0, alors l'équation quadratique admet :","option_a":"Une racine réelle double","option_b":"Deux racines réelles distinctes","option_c":"Aucune racine réelle","option_d":"Deux racines complexes","option_e":"","option_f":"","bonne_reponse":"B","explication":"Lorsque le discriminant est strictement positif (Δ \u003E 0), l'équation quadratique admet deux racines réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4935,"question":"La factorisation de x² - 5x + 6 est :","option_a":"(x - 2)(x - 3)","option_b":"(x + 2)(x + 3)","option_c":"(x - 1)(x - 6)","option_d":"(x + 1)(x + 6)","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 5x + 6 se factorise en (x - 2)(x - 3) car 2 et 3 sont les racines du trinôme (2 + 3 = 5 et 2 × 3 = 6).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4936,"question":"Si a = 0 dans un trinôme du second degré, alors il devient une équation du premier degré.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si a = 0, le trinôme se réduit à bx + c, qui est une équation du premier degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4937,"question":"Quelle est la valeur du discriminant pour l'équation x² - 4x + 4 = 0 ?","option_a":"0","option_b":"4","option_c":"8","option_d":"16","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x² - 4x + 4 = 0, Δ = b² - 4ac = (-4)² - 4(1)(4) = 16 - 16 = 0. Le discriminant est donc égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4938,"question":"La factorisation de 2x² - 8x + 6 est :","option_a":"2(x - 1)(x - 3)","option_b":"(2x - 2)(x - 3)","option_c":"2(x + 1)(x + 3)","option_d":"(x - 1)(2x - 6)","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x² - 8x + 6 = 2(x² - 4x + 3) = 2(x - 1)(x - 3). On factorise d'abord par 2, puis on applique l'identité remarquable.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4939,"question":"Si Δ = 0, alors l'équation quadratique admet une racine réelle double.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Lorsque le discriminant est égal à 0 (Δ = 0), l'équation quadratique admet une racine réelle double (racine double).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4940,"question":"Quelle est la somme des racines de l'équation x² - 7x + 10 = 0 ?","option_a":"5","option_b":"7","option_c":"10","option_d":"-7","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une équation quadratique ax² + bx + c = 0, la somme des racines est égale à -b\/a. Ici, -(-7)\/1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4941,"question":"La factorisation de x² + 6x + 9 est :","option_a":"(x + 3)²","option_b":"(x - 3)²","option_c":"(x + 3)(x - 3)","option_d":"(x + 1)(x + 9)","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² + 6x + 9 est un carré parfait : (x + 3)² = x² + 6x + 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]