MUODILAI KVADRATI

MUODILAI KVADRATI, muodi­lai namudi akh*+kh+s — 0-ro guyand, ki dar on a, , s adadhoi ikhtiyori buda, koeffisienthoi muodila no­mida meshavand. Muodilai kvadrati du resha do­rad, ki az rui formulahoi ^ _ — +U ‘—4as ¹          Ta ¹

b —U b^t—iae 2 a

hisob karda meshavand. Ifodai D = = ² — 4as diskriminanti Muodilai kvadrati no­mida meshavad. Agar D > 0 boshad, Muodilai kvadrati reshahoi haqiqii gunogun do­rad; agar D < 0 boshad, reshahoi Muodilai kvadratii adadhoi kompleksii ba hamdigar hamrohshuda (payvasta) meboshand; agar D * 0 boshad, Muodilai kvadrati doroi du re­shai haqiqii ba hamdigar barobar meboshad. Vobastagii bayni resha az koeffisienthoi Muodilai kvadratiro formulai Vieta J| + J2 = —b/a, kh\kh^ v cla

muayyan mekunad. Tarafi chapi Muodilai  kvadratiro dar namudi v(j — kh\) (j — —j₂) ifoda kardan mumkin ast. Funksiyai u = akh²+kh+s-ro seazoii kvadrati menomand, ki grafiki on az parabolai qullaash dar nuqtai M(—/2a; e—6²/4v) voqegashta va tiri simmetriyaash ba tiri Ou parallel iborat meboshad; sam- ti shokhahoi parabola bo alomati a yakkhela ast; Usulhoi geometrii hal­li Muodilai kvadrati az davrahoi qadim malum bud.