Awuqwalaselanga ulibele ukuba yokusombulula i'quadratic equation 'ayigqitywanga?

Indlela yokusombulula lo engaphelelanga i'quadratic equation? Yinto eyaziwayo ukuba kukho ngobuwena ethile ukulingana ngezembe ² + Bx + C = Owu, apho kukho, b kunye c - ke okuza yokuveliswa x ongaziwayo, emasikwini a ≠ o, kwaye b kunye c Kute - ngaxeshanye okanye ngokwahlukeneyo. Umzekelo, C = Owu, ku ≠ okanye ngolunye uhlobo. Siya sele kuphantse ukuba ukukhumbula ukuba inkcazo i'quadratic equation.

acacise

bolwesibini udidi Trinomial ilingana zero. lomlingani walo wokuqala libe ≠ o, b kunye c singathatha naliphi na inani. Ixabiso x bume ziya kuba ingcambu lenxaki, apho xa endaweni ithuba kwindawo ukulingana ezichanekileyo lwamanani. Makhe siqwalasele iingcambu zokwenene, nangona izigqibo quadratic kunokuba amanani ezintsonkothileyo. Zalisa ebizwa inxaki apho namnye okuza akalingani o, a ≠ o, a ≠ o, c ≠ o.
Thina ukusombulula umzekelo. 2 ² 5 = -9h-on, sifumana
D = 81 + 40 = 121,
D positive, iingcambu ke ngoko x ₁ = (9 + √121): 4 = 5, kwaye eyesibini x ₂ = (9-√121): kuyoze = 4, 5. Ukuqinisekiswa inceda ukuqinisekisa ukuba zichanekile.

Nantsi ke inyathelo sisombululo linyathelo i'quadratic equation

Ngenxa discriminant na ukusombulula nayiphi na lenxaki, kwicala lasekhohlo kuku a trinomial ezaziwayo-kakuhle square xa ≠ ngayo. Kumzekelo wethu. -9h-2 ² 5 0 = (s ² + Bx + C = O)

• Fumana lokuqala discriminant D yi eyaziwayo -4as ifomula ^2.
• Sihlole yintoni na ixabiso D: kufuneka ngaphezu zero ilingana zero okanye ngaphantsi.
• Siyazi ukuba xa D> o, i'quadratic equation uye iingcambu yokwenene ezahlukeneyo ezimbini kuphela, kodwa ngokuqhelekileyo ibonisa kwakhona x ₁ x _2,
  nantsi ukubala indlela:
  x ₁ = (-c √D +) :( 2a) kwaye okwesibini: x ₂ = (-ukuze-√D) :( 2a).
• D = o - enye ingcambu, okanye, yithini, lingana ezimbini:
  x ₁ ilingana ₂ kwaye -ukuba ngokulinganayo: (2a).
• Ekugqibeleni, D

Cinga into quadratic engaphelelanga bolwesibini udidi

1. kugawulwa ² + Bx = o. Sisimeli esingatshintshiyo, lomlingani c xa x ⁰ ilingana zero, a ≠ o.
   Indlela ukusombulula inxaki engaphelelanga equation 'yale hlobo? Thatha ngaphandle x kwizibiyeli. Sikhumbula xa imveliso miba mibini zero.
   x (izembe + b) = o, kusenokuba xa: X O okanye xa nezixholo + b = o.
   Ukukhetha 2 equation yomgama, sino 'x = -c / a.
   Ngenxa yoko, sinalo iingcambu x ₁ = 0, computationally x ₂ = -b / _a.
2. Ngoku 'ngumlingani ka' x 'ngayo, kodwa akalingani (≠) o.
   ² x + c = o. Ngaba uye kwicala lasekunene lenxaki, sifumana x ² = c. Le equation uye kuphela iingcambu lenene, xa inani c entle (c 'x' ulingana _no-1 xa √ (c), ngokulandelelana, x ₂ - -√ (c). Kungenjalo, inxaki awuveli kwaphela.
3. Le ndlela yokugqibela: b = c = o, okt ² s = o. Ngokuqhelekileyo, i'quadratic elula abanje lusuka omnye, x = on.

iimeko ezizodwa

Indlela yokusombulula i'quadratic equation ingqalelo ayiphelelanga, kwaye ngoku vozmem naluphi na uhlobo.

• Ngokupheleleyo quadratic equation yesibini lomlingani x - inani.
  Vumela k = o, 5b. Sinawo Ngokwefomyula yokubala discriminant kunye neengcambu.
  D / 4 ² = k - ac, iingcambu ukubalwa njengoko x _{1,2 = (-k ± √ (D} / 4)) / a xa D> o.
  x = -k / a kwi D = o.
  Akukho iingcambu xa D
• Banikwa quadratic equation 'xa' ngumlingani ka 'x' ophindwe 1, iye ukubhala x ² + p + q = o. Baya kuxhomekeke yonke indlela ngasentla, ukubala thile lula.
  Umzekelo ² x 9--4h = 0. yekhompyutha D: 2 ² +9, D = 13.
  = X ₁ 2 + √13, x ₂ = 2-√13.
• Ukongeza, kunikwa isicelo ngokulula i theorem ka Vieta. Uyatsho ukuba udibaniso esineengcambu alenxaki uyalingana -p, ngumlingani yesibini kunye minus (okuthetha umqondiso esahlukileyo), kwaye imveliso beengcambu ilingana q, sisimeli esingatshintshiyo. Khangela bekuya kuba njani lula vocally ukuchonga iingcambu zale nxaki. Kuba unreduced (ngokuba bonke okuza akalingani zero), le theorem lisetyenziswa ngolu hlobo lulandelayo: isixa x ₁ + x ₂ -ukuba ngokulinganayo / a, imveliso x ₁ · x ₂ ulingana / a.

Sum kwekota ngokwenene inomlingani wokuqala ulingana ngumlingani b. Kulo meko, inxaki lusuka enye ubuncinane (kwaba lula), kuqala efunekayo -1, kwaye eyesibini c / a, ukuba ikhona. Indlela yokusombulula i'quadratic equation 'ngu ayiphelelanga, uyakwazi zihlole. Simple. Le okuza inokuba kusenziwa ngokwemilinganiselo ethile nenye

• x ² + x = o, 7x ² -7 = o.
• Umdibaniso konke okuza imalunga.
  Iingcambu nxaki - 1 c / a. Umzekelo 2 ² -15h + 13 = o.
  ₁ = x 1, x ₂ = 13/2.

Kukho nezinye iindlela ezininzi zokusombulula iikoteshini ezahlukeneyo bolwesibini udidi. Umzekelo, indlela yokwabiwa Kule polynomial egqibeleleyo. ngeendlela ezininzi mfanekiso. Xa usebenza ngokufuthi ngemizekelo enjalo, bafunde indlela 'flip "bona nembewu, ngokuba zonke iindlela beza engqondweni ngokuzenzekelayo.