Tushen na wani quadratic lissafi: algebraic da kuma lissafi ma'anar

A aljabara square da aka kira a karo na biyu domin lissafi. By lissafi nufa a ilmin lissafi magana, wanda yana a cikin abun da ke ciki na ɗaya ko fiye ba a sani ba. Biyu-domin lissafi - a ilmin lissafi lissafi da ciwon akalla daya ba a sani ba a cikin square digiri. A quadratic lissafi - biyu-domin lissafi nuna ainihi don nufin daidaita da sifili. Warware da lissafi square ne guda cewa sanin da square tushen da lissafi. Hankula quadratic lissafi a general form:

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

cikinsa W, T - da coefficients na tushen da quadratic lissafi.

O - free coefficient.

c - tushen na quadratic lissafi (ko da yaushe yana biyu dabi'u C1 kuma C2).

Kamar yadda aka ambata riga, matsalar warware wani quadratic lissafi - gano tushen da wani quadratic lissafi. Don nemo su, kana bukatar ka sami wani discriminant:

N = T ^ 2 - 4 * W * Ya

A discriminant dabarbari zama dole domin samar da mafita tushen C1 kuma C2:

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

Idan quadratic lissafi na general nau'i factor a tushen T yana da wani mahara darajar, da lissafi aka maye gurbinsu:

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

Kuma saiwoyinsa kama da magana:

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

Sau da yawa lissafi iya samun wani dan kadan daban-daban bayyanar a lokacin da C_2 iya samun wani coefficient W. A wannan yanayin, sama lissafi yana da siffar:

c ^ 2 + F * c + L = 0

inda F - factor a tushen;

L - free factor.

c - tushen na da square (ko da yaushe yana biyu dabi'u C1 kuma C2).

Wannan irin lissafi da aka kira wani quadratic lissafi ba. Sunan "rage" tafi daga dabara actuation hankula quadratic lissafi, idan coefficient na W tushen yana da darajar da daya. A wannan yanayin, da tushen da quadratic lissafi:

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

A cikin hali na ko da dabi'u na coefficient na F tushen Tushen zai yi wani bayani:

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

Idan muka magana game da quadratic lissafai, shi wajibi ne don tunawa da Theorem na Vieta. Ya furta cewa, wadannan dokokin domin rage quadratic lissafi:

c ^ 2 + F * c + L = 0

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

A general quadratic lissafi quadratic lissafi tushen ne related dependencies:

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

C1 + C2 = -T / W kuma C1 * C2 = Ya / W

Yanzu la'akari da zabin na quadratic lissafai da su mafita. Dukan su iya zama biyu, kamar yadda idan wani memba na c_2 ya bace, sa'an nan da lissafi ba zai zama murabba'i. saboda haka:

1. W * c ^ 2 + T * c = 0 na quadratic lissafi embodiment ba tare da free factor (memba).

The bayani ne:

W * c ^ 2 = -T * c

C1 = 0, C2 = -T / W

2. W * c ^ 2 + O = 0 na quadratic lissafi embodiment ba tare da wa'adi na biyu, a lokacin da wannan modulo da tushen da quadratic lissafi.

The bayani ne:

W * c ^ 2 = -O

C1 = √ (-O / W), C2 = - √ (-O / W)

Duk wannan ya aljabara. Ka yi la'akari da lissafi ma'anar wanda yana da quadratic lissafi. na biyu domin lissafi a cikin lissafi ne aka bayyana ta a parabola aiki. quite sau da yawa aiki ne a sami tushen da wani quadratic lissafi ga makarantar sakandare dalibai? Wadannan Tushen ba manufar yadda za a rarraba jadawali aiki (parabola) tare da tsara axis - a kwance. Idan, bayan da ya yanke shawarar da quadratic lissafi, za mu samu da m yanke shawara na tushen, sa'an nan da mahada so ba. Idan tushen yana daya jiki darajar, da aiki crosses da x-axis a wuri guda. Idan biyu Tushen, sa'an nan, bi da bi, - maki biyu na rarrabawa.

Shi ne ya kamata a lura da cewa a karkashin m tushen nufa wani mummunan darajar karkashin tushen, a tushen binciken. Jiki darajar - wani tabbatacce ko korau darajar. A cikin hali na gano daya kawai tushen nufin cewa tushen da wannan. The fuskantarwa da kwana a wani Cartesian daidaita tsarin kuma za a iya pre-ƙaddara da coefficients na W tushen da kuma T. Idan W yana da wani m darajar, biyu rassan da parabola an fuskantar sama. Idan W yana da wani mummunan darajar, - zuwa ƙasa. Har ila yau, idan coefficient B yana da wani m ãyã, a cikinta W ne ma m, da kokuwa na parabola aiki ne a cikin "y" daga "-" don rashin iyaka "+" rashin iyaka, "c" a cikin kewayon debe rashin iyaka da sifili. Idan T - m darajar, kuma W - shi ne korau, a daya gefen da abscissa.