Kodi mwaiwala momwe mungathetsere kayendedwe ka quadratic equation?

Kodi mungathetse bwanji vuto losakwanira la quadratic equation? Zikudziwika kuti ndizosiyana kwambiri ndi ax2 + bx + c = a, pamene, b, ndi c zimakhala zenizeni zenizeni pa x osadziwika, ndipo ≠ a, ndi b ndi c ndi zeros, panthawi yomweyo kapena padera. Mwachitsanzo, c = o, mu ≠ o kapena mosiyana. Tatsala pang'ono kukumbukira tanthauzo la quadratic equation.

Tidzafotokozera

Utatu wa chiwerengero chachiwiri ndi wofanana ndi zero. Coefficient yoyamba ya ≠ o, b ndi c ingatengere miyezo iliyonse. Mtengo wa osinthika x udzakhala muzu wa equation, poika mmalo mwake, udzabwezeretsa kukulingana kwa chiwerengero choyenera. Tiyeni tipitirizebe kuwona mizu yeniyeni, ngakhale kuti mayankho a equation angakhale nambala zovuta. Ndizozoloŵera kuyitanira equation imene palibe coefficients yofanana ndi, ndi ≠ o, ku ≠ o, ndi ≠ o.
Tiyeni tikambirane chitsanzo. 2s ² -9c-5 = o, tikupeza
D = 81 + 40 = 121,
D imakhala yabwino, ndiye pali mizu, x ₁ = (9 + √121): 4 = 5, ndi yachiwiri x ₂ = (9-√121): 4 = -o, 5. Kufufuza kudzawathandiza kuonetsetsa kuti zowona.

Pano pali njira yothandizira ya quadratic equation

Kupyolera mwachisankho, mayina aliwonse angathe kuthetsedwa, kumanzere komwe kulipo quadratic trinomial kwa ≠ o. Mu chitsanzo chathu. 2х ² -9-5 = 0 (ах ² + вх + с = о)

• Choyamba timapeza chisankho cha D discriminant D mwachidziwitso chodziwika bwino mu ² -4as.
• Timayesa kuti mtengo wa D udzakhala wotani: tili ndi zoposa zero, ndi zofanana ndi zero kapena zosachepera.
• Tikudziwa kuti ngati D> o, mgwirizano wa quadratic uli ndi mizu yeniyeni yeniyeni yosiyana, imatchulidwa ndi x ₁ kawirikawiri ndi x ₂ ,
  Izi ndizowerengera:
  X ₁ = (-v + √D): (2a), ndi wachiwiri: x ₂ = (-in-√D): (2a).
• D = o ndi muzu umodzi, kapena, amati, awiri ofanana:
  X ₁ ndi x ₂ ndipo ndi ofanana ndi: mu: 2a).
• Pomaliza, D

Tiyeni tilingalire zomwe ziri zofanana zosagwirizana za digiri yachiwiri

1. Ah ² + mu x = o. Nthawi yomasuka, coefficient c ya x ⁰ , ndi zero apa, mu ≠ o.
   Mmene mungathetsere kusagwirizana kwa quadratic equation ya mtundu umenewu? Timatenga x pa mabakia. Timakumbukira pamene zotsatira za zinthu ziwiri ndi zero.
   X (nkhwangwa + b) = o, izi zikhoza kukhala pamene x = 0 kapena nkhwangwa + b = o.
   Kuthetsa lingaliro lachiwiri lofanana, tili ndi x = -v / a.
   Zotsatira zake, tili ndi mizu x ₁ = 0, Ndi mawerengedwe X ₂ = -b / a _.
2. Tsopano coefficient ya x ndi ofanana ndi o, ndipo c si ofanana ndi (≠) o.
   X ² + c = o. Timanyamula c ku mbali yeniyeni ya equation, timapeza x ² = -c. Kugwirizana kumeneku kuli ndi mizu yeniyeni pokhapokha -kakhala nambala yabwino (c X _{1 ndiye} ndiye ofanana ndi √ (-c), motsatira, x ₂ - -√ (-c). Apo ayi, equation ilibe mizu nkomwe.
3. Njira yotsiriza: b = c = o, ndiko, ^{2 2} = o. Mwachibadwa, kuphatikiza kosavuta kumakhala ndi muzu umodzi, x = o.

Milandu yapadera

Mmene mungathetsere chiwerengero chosagwirizana cha quadratic equation, ndipo tsopano tikutenga mtundu uliwonse.

• M'chigawo chokwanira cha quadratic, coefficient yachiwiri kwa x ndi nambala.
  Lolani k = o, 5b. Tili ndi mwayi wowerengera tsankho ndi mizu.
  D / 4 = k ² - ac, mizu imawerengedwa motere: x _1,2 = (-k ± √ (D / 4)) / a kwa D> o.
  X = -k / a kwa D = o.
  Palibe mizu ya D
• Pali zofanana zowonongeka, pamene coefficient ya x m'kati ndi 1, kawirikawiri imalembedwa x ² + px + q = o. Zonsezi zapamwambazi zimagwiritsidwa ntchito kwa iwo, kuwerengera ndi kosavuta.
  Chitsanzo, x ² -4x-9 = 0. Ganizirani D: 2 ² +9, D = 13.
  X ₁ = 2 + √13, x ₂ = 2-√13.
• Kuonjezera apo, chiwonongeko cha Vietnam chimagwiritsidwa ntchito mosavuta pa zomwe tatchulazi . Limanena kuti chiwerengero cha mizu ya equation ndi -p, yachiwiri coefficient ndi chizindikiro chosasintha (kutanthauza chizindikiro chosiyana), ndipo mankhwala a mizu yomweyo ndi ofanana, nthawi yaulere. Onani momwe zingakhalike zosavuta kuti muwone mizu ya mgwirizanowu. Osaphunzitsidwa (pakuti coefficients zonse sizifanana ndi zero) theorem iyi ikugwira ntchito motere: chiwerengero x ₁ + x ₂ ndi -a / a, chida x ₁ · x ₂ chifanana ndi c / a.

Chiwerengero cha ufulu waulere c ndi coefficient yoyamba ndi ofanana ndi coefficient b. Mkhalidwe uwu, equation ili ndi mizu imodzi (yosavuta kutsimikizira), yoyamba iyenera kukhala -1, ndipo yachiwiri ikhale c / a, ngati ilipo. Momwe mungathetsere kusagwirizana kwa quadratic equation, mukhoza kudzifufuza nokha. Wophweka kuposa wophweka. Zokwanira zingakhale zogwirizana pakati pawo

• X ² + x = o, 7 x ² -7 = o.
• Chiwerengero cha coefficients ndi o.
  Mizu ya mgwirizano uwu ndi 1 ndi c / a. Chitsanzo, 2x2 -15x + 13 = o.
  X ₁ = 1, x ₂ = 13/2.

Pali njira zingapo zothetsera zofanana zofanana. Pano, mwachitsanzo, ndiyo njira yolekanitsira malo onse opezeka kuchokera ku polynomial wopatsidwa. Pali njira zambiri zowonetsera. Nthawi zambiri mukamachita zitsanzozi, mudzaphunzira momwe mungayankhire ngati mbewu, chifukwa njira zonse zimabwera m'maganizo.