Xididdada isla'egta a saablay: macnaha aljabrada iyo joomateri

In square algebra waxaa lagu magacaabaa isla'eg Si labaad. By isla'egta tusinayaan muujinta a xisaabta, taas oo uu leeyahay in ay ka kooban of hal ama ka badan oo aan la garaneyn. Second-si isla'eg - isla'egta xisaabeed isagoo ugu yaraan hal oo aan la garaneyn in degrees square. isla'egta saablay - labaad-si isla'eg muujiyey aqoonsi in ay ka dhigan tahay si siman u eber. Xalliyaan square isla'egta waa la mid ah in lagu ogaado xididada square ee isla'egta. isla'egta saablay caadiga ah qaab guud:

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

diidanyihiin W, T - ee horgalaha ah xididdada isla'egta saablay;

O - Wehliyaha xor ah,

c - xidid ah saablay isla'egta (had iyo jeer waxay leedahay laba qiimeeyo C1 iyo C2).

Sida hore u soo sheegnay, dhibaatada of xalinta isla'egta a saablay - helo xididada isla'egta a saablay. Si aad uga hesho, waxaad u baahan tahay si aad u hesho discriminant ah:

N = T ^ 2 - 4 * W * O

The qaaciidooyinka discriminant lagama maarmaan u ah xal raadinta C1 xidid iyo C2:

C1 = (-T + √N) / 2 * C2 W iyo = (-T - √N) / 2 * W

Haddii isla'egta saablay foomka factor guud ee asalka u ah T waxay leedahay qiimo badan, isla'egta waxaa lagu bedelaa:

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

Oo xididdadiisuna eg hadal ah:

C1 = [-U + √ (U ^ 2-W * O)] / W iyo C2 = [-U - √ (U ^ 2-W * O)] / W

Inta badan isla'eg laga yaabaa in muuqaal yar oo kala duwan marka C_2 laga yaabaa in ay ma W. Wehliyaha Xaaladdan oo kale, isla'egta kor ku xusan ayaa foomka:

c ^ 2 + F * c + L = 0

halkaas oo F - factor ee xididka,

L - factor xor ah,

c - asalka u ah laba jibbaaran (had iyo jeer waxay leedahay laba qiimeeyo C1 iyo C2).

Noocan ah isla'egta waxaa lagu magacaabaa isla'egta a saablay siiyey. Magaca "hoos" ka tegey actuation formula isla'egta caadiga saablay, haddii Wehliyaha ee xididka W uu qiimo ah oo ka mid ah. Xaaladdan oo kale, xididdada isla'egta saablay:

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

In the case of qiimaha xataa Wehliyaha oo ka mid ah xididdada xidid F yeelan doonaan xal:

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

Haddii aan ka hadlo isleegyo saablay, waxaa lagama maarmaan ah inuu dib ugu yeerto Aragtida of Vieta. Wuxuu sidoo kale dhigayaa in sharciyada soo socda ee isla'egta hoos saablay:

c ^ 2 + F * c + L = 0

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

In isla'egta saablay guud xididdada isla'egta saablay waa tiirsanaanta la xiriira:

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

C1 + C2 = -T / C2 W iyo C1 * = O / W

Haddaba ka fiirsada fursadaha of isleegyo saablay iyo xalalka ay. Dhamaan iyaga ka mid ah waxay noqon kartaa laba, sida haddii xubin ka mid ah c_2 ka maqan, ka dibna isla'egta ma noqon doonto square. Sidaa darteed:

1. W * c ^ 2 + T * c = 0 of muuqashadii isla'egta saablay aan factor free (xubin).

Xalku waa:

W * c ^ 2 = -T * c

C1 = 0, C2 = -T / W

2. W * c ^ 2 + O = 0 of muuqashadii isla'egta saablay aan ereyga labaad, marka isku modulo xididdada isla'egta saablay.

Xalku waa:

W * c ^ 2 = -O

C1 = √ (-O / W), C2 = - √ (-O / W)

Waxaas oo dhan wuxuu ahaa aljebra. Tixgeli macnaha joomateri of taas oo uu leeyahay isla'egta a saablay. isla'eg Si labaad ee geometry waxa lagu tilmaamay by function parabola ah. marar badan hawsha waa in la helo xididada isla'egta a saablay ardayda dugsiga sare? xididdada Kuwani waxay ku siin fikirka ah sida ay u midaysan shaqada garaaf (parabola) la dhidibka duwo - siman ah. Haddii, isagoo go'aansaday isla'egta saablay, aan ka helno go'aanka aan buuxin ee xididada, ka dibna isgoyska maayo. Haddii xididku wuxuu leeyahay mid qiimo jirka, shaqada gudbaya-dhidibka x hal meel. Haddii labada xididada, ka dibna, siday u kala horreeyaan, - labo dhibcood ka mid ah isgoyska.

Waxaa xusid mudan in hoos xididdada aan buuxin tusinaysa qiimaha xun hoos xididka, at helidda xididka. qiimaha jirka - wax kasta oo qiime togan ama taban. In the case of helo xididka ka mid ah oo kaliya ka dhigan tahay in xididdada isku mid. orientation The ee xariiqa qallooca ayaa in nidaam Cartesian duwo sidoo kale la pre-go'aamin karaa by ee horgalaha ah xididdada W iyo T. Hadii W uu qiimo fiican, laba laamood parabola waxaa si toos ah kor. Haddii W qiime negative ah, - hoos. Sidoo kale, haddii Wehliyaha B wuxuu leeyahay calaamad wanaagsan, kuna waari dhexdeeda W sidoo kale waa ay wanaagsan tahay, vertex ee function parabola waa gudahood ah "y" ka "-" si xad la'aan "+" xad la'aan, "c" kala duwan ee xad jaray eber. Haddii T - qiimaha wanaagsan, iyo W - waa xun, dhinaca kale ee abscissa ah.