Hauna kukanganwa sei kugadzirisa quadratic mukana wokuti vanhu vanga zvisakakwana?

Kugadzirisa kukwana quadratic mukana wokuti vanhu vanga? Zvinozivikanwa kuti chimwe pachake vakaenzana demo ² + Bx + C = O, uko, b uye C - the coefficients chaiye zvausingazivi X, uye sezvamakaropafadzwa munhu ≠ iwe, uye, b uye cvari- razero - panguva kana voga. Somuenzaniso, C = O, mune ≠ kana vakutarisire. Tine dzinenge kuyeuka tsanangudzo quadratic mukana wokuti vanhu vanga.

tsanangura

Trinomial dhigirii wechipiri akaenzana razero. coefficient Its wokutanga ≠ iwe, b uye munenge anogona kutora chero ukoshi. Kukosha shanduka X zvichange pamudzi mukana wokuti vanhu vanga, apo kana kuchiiswa kuzvitengesa yakarurama kusanganiswa nekuenzana. Ngatikurukurei midzi chaiyo, kunyange zvazvo Zvaitongwa equations zvinogona dzakaoma nhamba. Pedzisa anonzi mukana wokuti vanhu vanga umo hapana coefficients haana kuenzana iwe, munhu ≠ Haiwa, munhu ≠ O, c ≠ o.
Isu yokugadzirisa muenzaniso. 2 ² 5 = -9h-mberi, tinowana
D = 81 + 40 = 121,
D ndiko zvakanaka, midzi zvino x ₁ = (9 + √121): 4 = 5, uye wechipiri X ₂ = (9-√121): -o = 4, 5. Verification kunobatsira nechokwadi kuti vari kwakarurama.

Heino danho nedanho mhinduro kune quadratic mukana wokuti vanhu vanga

Kuburikidza discriminant anogona kugadzirisa chero mukana wokuti vanhu vanga, kuruboshwe divi iri chinozivikanwa mativi trinomial apo ≠ pamusoro. In muenzaniso wedu. -9h-2 ² 5 0 = (s ² + Bx + C = O)

• Find wokutanga discriminant D kubudikidza anozivikanwa payakavakirwa ² -4as.
• Tiongorore chii kunokosha D: tine vanopfuura razero akaenzana razero zvichidzika.
• Tinoziva kuti kana D> iwe, munhu quadratic mukana wokuti vanhu vanga ane mbiri chete zvakasiyana midzi chaivo, ivo yemanyorero dzinomirira x ₁ uye X _2,
  heunoi sei kuverenga:
  x ₁ = (-c + √D) :( 2a) uye wechipiri: x ₂ = (yekuva-√D) :( 2a).
• D = O - imwe mudzi, kana, muti, vaviri vakaenzana:
  x ₁ akaenzana ₂ uye akaenzana yekuva: (2a).
• Pakupedzisira, D

Funga kukwana equations dzeboka rechipiri

1. demo ² + Bx = o. The Kugara rokuti, coefficient C kana X ⁰ akaenzana razero, mumwe ≠ o.
   Kugadzirisa kukwana quadratic mukana wokuti vanhu vanga kwakadai? Atore X ari mumabhuraketi. Tinorangarira kana zvinobikwa zviviri ndiyo razero.
   X (demo + b) = iwe, zvingava kana: X haiwa kana apo demo + b = o.
   Kusarudza 2nd Linear mukana wokuti vanhu vanga, tine x = -c / a.
   Somugumisiro, tine midzi x ₁ = 0, computationally X ₂ = -b / _a.
2. Zvino coefficient kuti X iri pamusoro, asi kwete kuenzana (≠) o.
   ² X + C = o. Ichaendeswa kurutivi rworudyi mukana wokuti vanhu vanga, tinowana X ² = c. mukana wokuti vanhu vanga ichi chete ane Midzi chaivo, kana yakanaka nhamba C (c X akaenzana ₁ kana √ (c), ukuwo, X ₂ - -√ (c). Zvikasadaro, mukana wokuti vanhu vanga haana midzi zvachose.
3. Yekupedzisira Ipfungwa: b = C = iwe, kureva ² s = o. Sezvingatarisirwa, yakadaro nyore shoma mukana wokuti vanhu vanga ane mudzi mumwe, x = pamusoro.

Special zviitiko

How kugadzirisa quadratic mukana wokuti vanhu vanga vaiona kukwana, uye ikozvino vozmem chero mhando.

• In zvizere quadratic mukana wokuti vanhu vanga chechipiri coefficient X - kunyange nhamba.
  Regai K = iwe, 5b. Tine nzira kuti pakuverenga ari discriminant uye midzi.
  D / 4 ² = k -; ac, midzi computed sezvo X _{1,2 = (-k ± √ (D} / 4)) / a kana D> o.
  x = -k / a pa D = o.
  No midzi kana D
• Vanopiwa quadratic equations apo coefficient kuti X akaenzana 1, vari kazhinji kunyora X ² + S. + q = o. Vari pasi ose pamusoro payakavakirwa, dzemaitirwe iri zvishoma nyore.
  Muenzaniso ² X 9--4h = 0. Compute D: 2 ² +9, D = 13.
  = X ₁ 2 + √13, X ₂ = 2-√13.
• Uyezve, vakapiwa nyore kushandisa mashoko theorem no kuti Vieta. Rinotaura kuti vakaverenga midzi mukana wokuti vanhu vanga akaenzana -p, wechipiri coefficient pamwe kubvisa (kureva pakatarisana chiratidzo), uye zvibereko midzi akaenzana Q, dzose izwi. Ongorora kuti zvaizova nyore sei kuva nemuromo tichidudza kuziva midzi mukana wokuti vanhu vanga ichi. For unreduced (nokuti coefficients zvose haana kuenzana razero), theorem no ichi rinoshandisirwa sezvinotevera: Verengai x ₁ + X ₂ akaenzana yekuva / a, chigadzirwa x ₁ · X ₂ akaenzana kuti / a.

Verengai kwakakwana izwi uye vokutanga coefficient uye akaenzana coefficient b. Pakadaro, mukana wokuti vanhu vanga ane mudzi mumwechete (akaratidza nyore), kutanga zvaida ari -1, uye yechipiri c / a, kana iripo. How kugadzirisa quadratic mukana wokuti vanhu vanga zvisakakwana, unogona kutarisa pachako. Simple. The coefficients kuve zvimwe zvikuru kune mumwe

• X ² + x = Haiwa, 7x ² -7 = o.
• Verengai coefficients zvose zviri pamusoro.
  Midzi mukana wokuti vanhu vanga ichi - 1 uye c / a. Muenzaniso 2 ² -15h + 13 = o.
  ₁ = x 1, X ₂ = 13/2.

Pane dzakawanda dzimwe nzira kugadzirisa equations siyana dzeboka rechipiri. Somuenzaniso, kuti nzira hurumende ichiisa ichi polynomial akakwana dzomumusha. Several graphical nzira. Kana kazhinji kubata mienzaniso yakadaro, kudzidza "pafiripi" navo sezvo mbeu, nokuti nzira dzose vanouya mupfungwa kwaita.