Ifayela echaza ifomu Vieta futhi kancane umlando

Vieta theorem - wawuyinto esikoleni cishe wonke umuntu. Kodwa kungaba "ajwayelekile" ngempela? Bambalwa sihlangana nabo ekuphileni kwansuku zonke. Kodwa akubona bonke labo abezwa izibalo, ngezinye izikhathi ngokugcwele incazelo ejulile futhi ukubaluleka okukhulu kwalesi theorem.

Vieta theorem lula kakhulu inqubo ukuxazulula lenqwaba nezinkinga zezibalo okwagcina ubilise phansi ukuba zixazulule ezothando quadratic :

ax2 + Bx + c = 0, lapho ≠ 0.

Lona fomu esezingeni ezothando quadratic. Ezimweni eziningi, ezothando quadratic anjalo okuza a, b, c, okungase kalula lula sokuhlukanisa wawayisa. Kulokhu, sifika kusho ezothando quadratic, ebizwa ngokuthi encishisiwe (lapho Coefficient lokuqala kwesibalo ilingana 1):

X2 + px + q = 0

Kuyinto kulolu hlobo of zibalo futhi evumelana ukuyisebenzisa theorem ka Vieta. The main umqondo theorem wukuthi abakuzuzile izimpande kv.uravneniya inikezwe ngomlomo kungaba azimisele kalula kokwazi maqondana eziyisisekelo Theorem:

• isamba izimpande ilingana nenani okuphambene Coefficient wesibili (isib -p);
• umkhiqizo uyalingana Isici sesithathu (ie, q).

Okungukuthi, x1 + x2 = -p, futhi x1 * x2 = q.

Isinqumo seningi izinkinga izibalo esikoleni kuyehla kube pair elula lwezinombolo atholakala kalula ngesikhathi esincane amakhono ifa ukubala ngomlomo. Futhi akufanele kusenze izinkinga. Kukhona theorem ephambene Vieta ivumela pair ezikhona izinombolo, okuyizinto izimpande ezothando quadratic, kulula ukubuyisela okuza yayo nokubhala ngefomu ejwayelekile.

Ikhono ukusebenzisa Vieta theorem njengoba ithuluzi kakhulu kuyakunciphisa nezinkinga zezibalo kanye ngokomzimba ngokuhamba esikoleni esiphakeme. Ikakhulukazi lokhu kuyikhono lubaluleke ekulungiseleleni abafundi amakilasi abaphezulu ukuhlolwa.

Eqaphela ukubaluleka ithuluzi zezibalo elula nephumelelayo ezinjalo, ngangilokhu cabanga ngendoda, okokuqala uyivule.

Fransua Viet - isazi sesayensi esidumile isiFulentshi, owaqala umsebenzi wakhe ummeli. Kodwa, kusobala, izibalo Kwakungu ukubizwa kwakhe. Nakuba enkonzweni yasebukhosini njengoba kumeluleki, waba abadumile, wakwazi ukufunda i abamba umlayezo oyimfihlo we-King of Spain eNetherlands. Lokhu Yasinika inkosi French uHenry III ithuba ukwazi zonke izinhloso kwabaphikisi bakhe.

Kancane kancane, isingeniso ilwazi leembalo, Fransua Viet wafinyelela esiphethweni ukuthi kumelwe ukuba ukhona buhlobene eduze zakamuva ngesikhathi nophenyo "algebraists" futhi ziyinto eyigugu ezijulile weJiyomethri lasendulo. Ngokuhamba ucwaningo lwesayensi wayeklanyelwe futhi owasungulwa cishe yonke algebra aphansi. Waqale kuqalwe kusetshenziswe ama-amagugu elingokoqobo apharathasi zezibalo, kunomahluko ocacile phakathi nomqondo inombolo, futhi ukubaluleka nobuhlobo babo. Wyeth wabonisa ukuthi ngokwenza imisebenzi ifomu ongokomfanekiso, ungakwazi ukuxazulula le nkinga esimweni jikelele, ngoba cishe wonke amanani lamanani ecacisiwe.

Ucwaningo lwakhe ukuxazulula zibalo ezingaphezu kuka yesibili, kuholele theorem manje eselaziwa ngokuthi generalized Theorem ka Vieta. It has a okukhulu okusebenzayo kanye nokusebenza kwayo kwenza isixazululo okusheshayo zibalo umyalelo ephakeme.

Omunye izakhiwo lokhu theorem simiswe ngalendlela lelandzelako: umkhiqizo zonke izimpande ngezinga n-th ilingana emalungwini alo khulula. Le mpahla ngokuvamile sisetshenziswa ukuxazulula zibalo idigri lesithathu noma lesine ngenhloso ukwehlisa umyalelo we polynomial. Uma polynomial degree n-th elisuka inamba, zingase kalula ekhonjwe yi-Ukukhetha elula. Futhi okunye, ngokwenza division polynomial elithi (x1-x), a polynomial (n-1) th degree.

Ekugcineni, siphawula ukuthi theorem Vieta ingenye edume kakhulu theorems esikoleni algebra Yiqiniso. Igama lakhe kuthatha liyindawo efanelekayo phakathi amagama zezibalo okukhulu.