Awuzange ukhohlwe indlela yokuxazulula ezothando quadratic akuphelele?

Indlela ukuxazulula akuphelele equation Quadratic? Kuyaziwa ukuthi kuba samuntu oluthile ukulingana ngembazo ² + Bx + C = O, eyaziwa lapho a, b futhi c - the okuza wangempela x engaziwa, futhi lapho umuntu ≠ o, futhi b futhi c kukhona zero - kanyekanye noma ngokwehlukana. Ngokwesibonelo, C = O, endaweni ≠ noma okuphambene nalokho. Sesikhathele cishe kuzo ukuze bakhumbule isidlo incazelo equation Quadratic.

ukucacisa

besigaba sesibili Trinomial ilingana no-zero. Coefficient sayo sokuqala ≠ o, b futhi c kungathatha akubaluleke ngalutho. Inani x variable liyobe empandeni equation, lapho lapho ukufaka endaweni ithuba bayifaka lesifanele ukulingana kwamanani. Ake sicabangele imisuka yangempela, nakuba izinqumo zibalo kungaba eqela. Cedzela ngokuthi i equation lapho noyedwa okuza akulingani o, a ≠ o, a ≠ o, c ≠ o.
Thina ukuxazulula isibonelo. 2 ² 5 = -9h-ku, sithola
D = 81 + 40 = 121,
D inguyebo, izimpande ke x ₁ = (9 + √121): 4 = 5, kanti eyesibili x ₂ = (9-√121): -O = 4, 5. Ukuqinisekiswa kwe kusiza ukuqinisekisa ukuthi baqinisile.

Nasi isinyathelo ngesinyathelo isixazululo kuya equation Quadratic

Ngokusebenzisa discriminant ungakwazi ukuxazulula equation, ohlangothini lwesobunxele kuyinto trinomial square owaziwa lapho ≠ obakhathalelayo. Ngo Isibonelo sethu. ^-9h-2 2 5 0 = (s ² + Bx + C = O)

• Thola kuqala discriminant D yi eyaziwa ifomula ² -4as.
• Sibheka ukuthi yini ukubaluleka D: esinalo ezingaphezu kuka-zero ilingana zero noma ngaphansi.
• Siyazi ukuthi uma D> o, ezothando quadratic elisuka yangempela ezahlukene ezimbili kuphela, ngokuvamile zimelela x ₁ kanye x _2,
  nakhu ukuthi ukubala:
  x ₁ = (-c + √D) :( 2a) kanti eyesibili: x ₂ = (Lokudlulisa √D) :( 2a).
• D = o - eyodwa izimpande, noma, engiyishoyo, amabili alinganayo:
  x ₁ ilingana nenani ₂ futhi Lokudlulisa alinganayo: (2a).
• Ekugcineni, D

Cabanga ngalokho kukhona zibalo akuphelele besigaba sesibili

1. ngembazo ² + Bx = o. Igama elithi njalo, Coefficient c lapho x ⁰ ilingana no-zero, i-≠ o.
   Indlela ukuxazulula akuphelele equation Quadratic zalolu hlobo? Khipha x kubakaki. Siyakhumbula lapho umkhiqizo izici ezimbili zero.
   x (imbazo + isibekiwe b) = o, kungase lapho: X O noma lapho imbazo + b = o.
   Ukunquma 2nd kwesibalo yomugqa, sinalo x = -c / a.
   Ngenxa yalokho, siba izimpande x ₁ = 0, computationally x ₂ = -B / _a.
2. Manje Coefficient x imayelana, kodwa akulingani (≠) o.
   ² x + c = o. Kuzoya ohlangothini lwesokunene equation, sithola x ² = c. Lokhu kwesibalo elisuka yangempela kuphela, lapho omuhle inombolo c (c x ilingana ₁ uma √ (c), ngokulandelana, x ₂ - -√ (c). Kungenjalo, kwesibalo ayinakho izimpande nhlobo.
3. Inketho zokugcina: b = c = o, okusho ² s = o. Ngokwemvelo, ezothando enjalo elula kancane has eyodwa izimpande, x = ku.

Ezimweni Special

Indlela ukuxazulula ezothando quadratic kubhekwe akuphelele, futhi manje vozmem yiluphi uhlobo.

• Ngokugcwele quadratic equation yesibili Coefficient x - ngisho inombolo.
  Ake k = o, 5b. Sinazo ifomula ukubala discriminant nezimpande.
  D / 4 ² = k - ac, izimpande ngekhompyutha njengoba x _{1.2 = (-k ± √ (D} / 4)) / a uma D> o.
  x = -k / a ngesikhathi D = o.
  Ayikho izimpande uma D
• Banikwa zibalo quadratic lapho Coefficient x yisikwele 1, ngokuvamile ukurekhoda x ² + p + q = o. Ziyakwazi kuncike yonke ifomula ngenhla, ukubala Kuthi elula.
  Isibonelo ² x 9--4h = 0. yekhompyutha D: 2 ² +9, D = 13.
  = X ₁ 2 + √13, x ₂ = 2-√13.
• Ngaphezu kwalokho, unikezwa balusebenzise kalula theorem ka Vieta. Lithi isamba izimpande kwesibalo ilingana -p, Coefficient wesibili ne lokususa (okusho ukuthi uphawu okuphambene), futhi umkhiqizo ezimpandeni ilingana q, igama elithi njalo. Hlola ukuthi kungaba lula kanjani ube vocally ukuhlonza izimpande zalesi equation. Ukuze unreduced (kuwo wonke ama-coefficient akulingani zero), lokhu theorem usetshenziswa ngale ndlela elandelayo: isamba x + ₁ x ₂ -ukuze alinganayo / a, umkhiqizo x ₁ · x ₂ okulingana / a.

Isamba eside ngokuphelele futhi Coefficient kuqala futhi ilingana b Coefficient. Kulesi simo, ezothando has impande okungenani oyedwa (wazibonakalisa kalula), edingekayo yokuqala -1, kanye c yesibili / a, uma ikhona. Indlela ukuxazulula ezothando quadratic akuphelele, ungabheka ngokwakho. Simple. I okuza kungenzeka ngezabelo ezithile nomunye

• x ² + x = o, 7x ² -7 = o.
• Inani lawo wonke ama-coefficient imayelana.
  Izimpande lokhu equation - 1 kanye c / a. Isibonelo 2 ² -15h + 13 = o.
  ₁ = x 1 x ₂ = 13/2.

Kunezinye izindlela eziningana ukuze uxazulule izibalo ezahlukene besigaba sesibili. Ngokwesibonelo, indlela yokwabiwa walesi sikwele ephelele polynomial. izindlela eziningana sokuqhafaza. Lapho ngokuvamile ekubhekaneni izibonelo ezinjalo, ufunde indlela "flip" kubo njengoba imbewu, ngoba zonke izindlela oyofika engqondweni ngokuzenzakalelayo.