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Para cada uno de los siguientes polinomios indica qué números racionales son candidatos a ser raíces suyas y, después, determina cuáles lo son:

a) 3x^2 + 4x + 5

b) 2x^3 + 9x^2 + 12x + 2

","status","pending_classification","hasRelatedVideo","relatedVideos",[133],{"_134":135,"_153":154,"_51":169,"_203":204,"_221":170},"content",{"_43":136,"_55":137,"_138":-5,"_139":140,"_141":142,"_143":-5,"_45":144,"_147":148,"_149":148,"_150":-5,"_151":152},"468e3e62-35e0-47be-a15f-68dd43bb32bb","Óptica Geométrica - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","fa6aaf42-4cc4-4d76-8915-7a67081f7e9a","user_id",{"_145":146},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_155":156,"_162":163,"_164":165,"_166":167,"_28":168},"provider",{"_43":157,"_158":159,"_160":161},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","d80487a0-0f98-42c8-99bb-551165ba3068","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/levels.m3u8",[170],{"_43":171,"_55":172,"_57":173,"_174":175,"_176":-5,"_147":177,"_149":177,"_45":178,"_151":173,"_184":185},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","2025-04-29T01:56:45.284172+00:00",{"_179":180,"_181":88,"_182":183},"childrenCount",18,"content_count","question_count",135489,"children",[186],{"_43":187,"_55":188,"_57":189,"_174":175,"_176":171,"_147":190,"_149":190,"_45":191,"_151":194,"_184":195},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_179":192,"_181":88,"_182":193},10,19948,"mecanica-2",[196],{"_43":197,"_55":79,"_57":80,"_174":175,"_176":187,"_147":198,"_149":198,"_45":199,"_151":201,"_184":202},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_179":88,"_181":88,"_182":200},3376,"resistencia-dos-materiais-4",[],"video",{"_43":142,"_13":137,"_138":-5,"_205":206,"_207":208,"_28":-5,"_209":-5,"_155":208,"_210":211,"_166":-5,"_212":-5,"_213":-5,"_214":-5,"_215":-5,"_45":216,"_217":88,"_218":-5,"_128":219,"_147":220,"_149":220},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_145":146},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[224,254,272],{"_40":225,"_42":41,"_43":226,"_101":227,"_125":242,"_126":243,"_51":244},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[228,231,234,237,240],{"_43":229,"_105":106,"_107":230},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":232,"_105":111,"_107":233},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":235,"_105":115,"_107":236},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":238,"_105":119,"_107":239},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":225,"_105":123,"_107":241},"y'' - 2y' + 6y = 0","Somente em y''−2y'+6y=0 o polinômio característico r²−2r+6=0 tem Δ<0, gerando raízes complexas conjugadas (1±i√5) e, portanto, solução em termos de exponencial modulando seno e cosseno. Nos demais itens (a–d) o discriminante é ≥0, produzindo raízes reais (distintas ou repetidas).","

Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

",[245],{"_43":246,"_55":247,"_57":248,"_174":175,"_176":249,"_147":250,"_149":250,"_45":251,"_151":248},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_179":252,"_181":88,"_182":253},4,12302,{"_40":255,"_42":41,"_43":256,"_101":257,"_125":269,"_126":270,"_51":271},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[258,261,264,266],{"_43":259,"_105":106,"_107":260},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":262,"_105":111,"_107":263},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":255,"_105":115,"_107":265},"

Verdadeiro, falso, verdadeiro

",{"_43":267,"_105":119,"_107":268},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","85,5 % decomposto → 14,5 % restante.\nN/N0 = 0,145 ⇒ t = ln(1/0,145)/(ln2/5730) ≈ 1,6×10⁴ anos.\nItens prováveis: (1) resta 14,5 % do C-14 (V); (2) idade ≈ 1,2×10⁴ anos ou 3 meias-vidas (F); (3) t½ do C-14 = 5730 anos (V). Sequência: V-F-V, correspondendo à alternativa c.","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[245],{"_40":273,"_42":41,"_43":274,"_101":275,"_125":290,"_126":291,"_51":292},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[276,279,282,284,287],{"_43":277,"_105":106,"_107":278},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":280,"_105":111,"_107":281},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":273,"_105":115,"_107":283},"Indeterminado",{"_43":285,"_105":119,"_107":286},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":288,"_105":123,"_107":289},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Os polinômios e números fornecidos estão corrompidos (símbolos “????”), impossibilitando aplicar Ruffini e concluir se são raízes. Sem dados completos, o problema é indeterminado.","Emplea la regla de Ruffini para dictaminar si los siguientes números son o no raíces de los polinomios citados:
a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[245],[245,294,303,309,313,314,315,323,328,336,337,342,348],{"_43":295,"_55":296,"_57":297,"_174":175,"_176":298,"_147":190,"_149":190,"_45":299,"_151":302},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_179":300,"_181":88,"_182":301},5,30614,"engenharia-mecatronica-1",{"_43":304,"_55":79,"_57":80,"_174":175,"_176":305,"_147":306,"_149":306,"_45":307,"_151":308},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_179":88,"_181":88,"_182":200},"resistencia-dos-materiais-6",{"_43":305,"_55":188,"_57":189,"_174":175,"_176":295,"_147":250,"_149":250,"_45":310,"_151":312},{"_179":300,"_181":88,"_182":311},25741,"mecanica-3",{"_43":171,"_55":172,"_57":173,"_174":175,"_176":-5,"_147":177,"_149":177,"_45":178,"_151":173},{"_43":197,"_55":79,"_57":80,"_174":175,"_176":187,"_147":198,"_149":198,"_45":199,"_151":201},{"_43":316,"_55":317,"_57":318,"_174":175,"_176":298,"_147":190,"_149":190,"_45":319,"_151":322},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_179":320,"_181":88,"_182":321},21,45865,"engenharia-civil-3",{"_43":249,"_55":324,"_57":325,"_174":175,"_176":298,"_147":190,"_149":190,"_45":326,"_151":327},"Engenharia de Petróleo","engenharia-de-petroleo",{"_179":300,"_181":88,"_182":253},"engenharia-de-petroleo-1",{"_43":329,"_55":330,"_57":331,"_174":175,"_176":316,"_147":332,"_149":332,"_45":333,"_151":335},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_179":300,"_181":88,"_182":334},8852,"estruturas-1",{"_43":187,"_55":188,"_57":189,"_174":175,"_176":171,"_147":190,"_149":190,"_45":191,"_151":194},{"_43":338,"_55":79,"_57":80,"_174":175,"_176":246,"_147":339,"_149":339,"_45":340,"_151":341},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_179":88,"_181":88,"_182":200},"resistencia-dos-materiais-7",{"_43":343,"_55":344,"_57":80,"_174":175,"_176":329,"_147":345,"_149":345,"_45":346,"_151":347},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_179":88,"_181":88,"_182":200},"resistencia-dos-materiais-5",{"_43":298,"_55":349,"_57":350,"_174":175,"_176":-5,"_147":351,"_149":351,"_45":352,"_151":350},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_179":353,"_181":88,"_182":354},29,351586,"tagsTree",[170,357],{"_43":298,"_55":349,"_57":350,"_174":175,"_176":-5,"_147":351,"_149":351,"_45":352,"_151":350,"_184":358},[359,365,371],{"_43":295,"_55":296,"_57":297,"_174":175,"_176":298,"_147":190,"_149":190,"_45":299,"_151":302,"_184":360},[361],{"_43":305,"_55":188,"_57":189,"_174":175,"_176":295,"_147":250,"_149":250,"_45":310,"_151":312,"_184":362},[363],{"_43":304,"_55":79,"_57":80,"_174":175,"_176":305,"_147":306,"_149":306,"_45":307,"_151":308,"_184":364},[],{"_43":316,"_55":317,"_57":318,"_174":175,"_176":298,"_147":190,"_149":190,"_45":319,"_151":322,"_184":366},[367],{"_43":329,"_55":330,"_57":331,"_174":175,"_176":316,"_147":332,"_149":332,"_45":333,"_151":335,"_184":368},[369],{"_43":343,"_55":344,"_57":80,"_174":175,"_176":329,"_147":345,"_149":345,"_45":346,"_151":347,"_184":370},[],{"_43":249,"_55":324,"_57":325,"_174":175,"_176":298,"_147":190,"_149":190,"_45":326,"_151":327,"_184":372},[373],{"_43":246,"_55":247,"_57":248,"_174":175,"_176":249,"_147":250,"_149":250,"_45":251,"_151":248,"_184":374},[375],{"_43":338,"_55":79,"_57":80,"_174":175,"_176":246,"_147":339,"_149":339,"_45":340,"_151":341,"_184":376},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários