Iingcambu i'quadratic equation: intsingiselo aljibra nezejometri

Xa algebra square kuthiwa umyalelo quadratic yesibini. Xa equation thile Ukuzibonakalisa ngokwezibalo, ethe kumafa yayo enye okanye engaziwayo ngaphezulu. Okwesibini-oda equation - i'quadratic zezibalo ukuba omnye ubuncinane ayaziwa nangomlinganiselo square. Quadratic equation - yesibini-order equation eboniswe ungubani lithetha ulingana zero. Sombulula isikwere equation iyafana ezibonakalisa iingcambu isikweri nxaki. quadratic equation gumbini ngendlela jikelele:

W * c ^ 2 + T * c + O = 0

kuyo W, T - ke okuza esineengcambu i'quadratic equation;

O - apaka free;

c - ingcambu ye equation equation (usoloko C1 amaxabiso amabini kunye nesiHlomelo C2).

Njengoko sele kukhankanyiwe, ingxaki yokusombulula i'quadratic equation '- ukufumana iingcambu i'quadratic equation. Ukuze ufumane kubo, kufuneka ukuba ufumane discriminant:

N = T ^ 2 - 4 * W * O

Le fomyula discriminant eziyimfuneko ukufumana izisombululo iingcambu C1 no-C2:

C1 = (-t + √N) / 2 * C2 W kwaye = (-t - √N) / 2 * W

Ukuba i'quadratic equation le jikelele ifomu factor kwi ingcambu T ixabiso ezininzi, inxaki esikhundleni:

W * c ^ 2 + 2 * U * c + O = 0

Kunye neengcambu zawo khangela ngathi la mazwi:

C1 = [-U + √ (U ^ 2-W * O)] / W no-C2 = [-U - √ (U ^ 2-W * O)] / W

Amaxesha amaninzi equation usenokuba imbonakalo eyahlukileyo kancinci xa C_2 ukuze bangabi W. lomlingani Kulo mzekelo, inxaki ngasentla ifomu:

c ^ 2 + F * c + L = 0

apho F - factor kwi ingcambu;

L - factor free;

c - ingcambu ye isikwere (usoloko C1 amaxabiso amabini kunye nesiHlomelo C2).

Olu hlobo alenxaki kuthiwa quadratic equation elinikiweyo. Igama "lifinyele" Wemka actuation indlela eqhelekileyo quadratic equation, ukuba ukungavumelani kwe ingcambu W has ixabiso enye. Kulo mzekelo, iingcambu i'quadratic equation:

C1 = -F / 2 + √ [(F / 2) ^ 2-L)] kunye ne-C2 = -F / 2 - √ [(F / 2) ^ 2-L)]

Kwimeko amaxabiso nditsho 'ngumlingani ka F ingcambu iingcambu ziya kuba isisombululo:

C1 = -F + √ (F ^ 2-L) C2 = -F - √ (F ^ 2-L)

Ukuba sithetha quadratic equation ', kuyimfuneko ukuba ukukhumbula theorem ka Vieta. Uyatsho ukuba imithetho zilandelayo i'quadratic equation kwanciphisa:

c ^ 2 + F * c + L = 0

C1 + C2 = -F kunye C1 * C2 = L

Xa quadratic equation jikelele iingcambu i'quadratic equation zezi izixhomekeki ezinxulumene:

W * c ^ 2 + T * c + O = 0

C1 + C2 = -t / W kunye C1 * C2 = O / W

Ngoku cinga iinketho quadratic equation 'kunye nezisombululo zazo. Bonke nga babini, ngokungathi ilungu c_2 ilahlekile, ngoko akayi kuba square inxaki. ke:

1. W * c ^ 2 + T * c = 0 lenxaki ngobuwena equation ngaphandle factor mahala (ilungu).

Isisombululo:

W * c ^ 2 = -t * c

C1 = 0, C2 = -t / W

2. W * c ^ 2 + O = 0 lenxaki ngobuwena equation ngaphandle kwekota yesibini, xa enye modulo iingcambu i'quadratic equation.

Isisombululo:

W * c ^ 2 = kodwa kuyoze

C1 = √ (kuyoze / W), C2 = - √ (kuyoze / W)

Konke oku kwaba algebra. Cinga intsingiselo zejometri lwalo quadratic equation. umyalelo equation yesibini geometry ichazwa umsebenzi parabola. kaninzi lo msebenzi ukufumana iingcambu i'quadratic equation 'ukuba abafundi bezikolo eziphakamileyo? Ezi iingcambu ukunika ingqikelelo ku gqiba njani umsebenzi grafu i (parabola) kunye nokulungelelanisa axis - tye. Ukuba, akuba wagqiba quadratic equation, sifumana isigqibo ngqiqweni yeengcambu, ngoko ke kwisiphambuka angeke. Ukuba iingcambu umntu ixabiso mnye, umsebenzi inqumle x-axis kwindawo enye. Ukuba iingcambu ezimbini, ngoko, ngokulandelelana, - iingongoma ezimbini yonqumlo.

Kubalulekile ukuphawula ukuba phantsi iingcambu engenangqondo kubonisa ixabiso athabathayo ingcambu, kwi ingcambu iziphumo. ixabiso Physical - naliphi na ixabiso entle okanye embi. Kwimeko lokufumana iingcambu enye kuphela kuthetha ukuba iingcambu efanayo. Imbonakaliso le ndawo curve kwinkqubo cartesian isilungelelanisi kwakhona pre-emiselwe okuza esineengcambu W kunye T. Ukuba W ibe lixabiso elingqinelanayo, kwamasebe amabini parabola zibhekiswe phezulu. Ukuba W has esinentlawulo engenaxabiso, - ezantsi. Kwakhona, ukuba lomlingani B unalo uphawu oluvumelanayo, apho W Yinkqubo eneziphumo ezihle, ke enekona lomsebenzi parabola yi ngaphakathi 'y' ukusuka '-' infinity "+" Infinity, 'c' ku ezahlukene thabatha Infinity eqandeni. Ukuba T - ixabiso HIV, kwaye W - lelikhabayo, kwelinye icala abscissa.