MUODILAI ALGEBRAVI

MUODILAI ALGEBRAVI, muodi­lai namudi /_p—0-ro guyand, ki dar on /_p bisyoruzvai darajai n-umi yak yo bisyortagyiryobandador (baroi l>0) ast. Muodilai algebrai yaknomaluma na­mudi zerin dorad:

a₀kh* v|Kh^l“* + … + a_p = 0,      (1)

in jo p — adadi butuni gayriman­fi, «o, A|, …, e_n — koeffisi­ent h o i muodila (adadhoi do­dashuda), kh — nomalumi matlub. Farz kardem, ki na hamai koeffisienthoi Muodilai algebravi (1) barobari sifrand. Agar a₀ =z£ 0 boshad, p-o d a r a j a i muodila menomand. On qimathoi nomalumi kh, ki muodi­lai (1)-ro qone megardonad, yane hangomi ba joi kh guzoshtani in qi- matho muodila ba ayniyat tabdil meyobad, reshahoi muodilai (1), inchunin reshahoi bisyoruzvai

/(kh)=a₀*^p+v|*^p’”^,+ ••• +^vp *0(2) nomida meshavand.

Vazifai asosii nazariyai muodilahoi algebravi justuju namudani reshahoi muodila meboshad. Baroi ifoda kardani reshahoi muodilahoi darajai 1, 2, 3 va 4 formulaho yof­ta shudaand, ammo baroi muodilahoi darajaashon az 4 bolo in guna for­mulaho dar shakli umumi mavjud nestand. Muodilai koeffisienthoyash kompleksii (2) yakjoya bo Muodilai algebravi (1), ki doroi l resha meboshad (nigarkd Teoremai asosii algebra), muoina karda shavad, sistemai muodilahoi algebravi hosil meshavad. Majmui hamai reshahoi in guna sistemaro bisyorshaklai (gunogunshaklai) al­gebravi menomand. Bisyorshaklahoi algebravi mavzui tadqiqoti geometriyai algebravi meboshad.

Adabiyot: K u r o sh . G., Kurs vieshey al­gebri, 11 izdanie., Moskva, 1975.