Koj tsis nco qab li cas los daws qhov kev ua tsis tiav quadratic?

Yuav ua li cas los daws kom tau tsis tau ua tiav quadratic equation? Nws paub tias nws yog ib qho kev hloov ntawm kev sib txuam ax2 + bx + c = a, qhov twg a, b thiab c yog cov coefficients rau x, thiab qhov twg a ≠ a, thiab b thiab c yog zeros, ib txhij lossis cais. Piv txwv, c = o, nyob rau hauv ≠ o los yog vice versa. Peb yuav luag nco txog lub ntsiab lus ntawm ib qho kev ua quadratic.

Peb yuav qhia ntxiv

Tus trinomial ntawm qib thib ob yog sib npaug rau xoom. Nws thawj coefficient a ≠ o, b thiab c yuav ua tau qhov tseem ceeb. Tus nqi ntawm nce mus nce los x yuav ces yuav lub hauv paus ntawm kab zauv, qhov twg thaum pawg tig nws mus rau hauv qhov tseeb hais txog zauv koob pheej ntawm lawv. Cia peb xav txog qhov tiag tiag hauv paus hniav, txawm hais tias tus txiav txim siab ntawm qhov sib npaug yuav ua tau cov lej nyuaj. Nws yog txoj kev cai hu rau qhov sib npaug ntawm qhov tsis muaj cov coefficients sib npaug li ib, thiab ≠ o, to ≠ o, nrog ≠ o.
Cia ua ke piv txwv. 2 ² 5 = -9h-on, peb yuav nrhiav tau
D = 81 + 40 = 121,
D yog zoo, cov hauv paus hniav ces x ₁ = (9 + √121): 4 = 5, thiab lub thib ob x ₂ = (9-√121): -o = 4, 5. Kev kuaj xyuas yuav pab kom paub tseeb tias lawv muaj tseeb.

Ntawm no yog ib txoj hauv kev daws cov kab quadratic

Los ntawm kev ntxub ntxaug, txhua qhov kev daws teeb meem daws tau, nyob rau sab laug ntawm uas muaj ib qho kev ntsuas quas qis rau ib qho ≠ o. Hauv peb tus qauv. -9h-2 ² 5 0 = (s ² + bx + C = O)

• Nrhiav thawj discriminant D los ntawm cov paub mis ² -4as.
• Peb xyuas seb tus nqi D yuav ua li cas: peb muaj ntau tshaj xoom, nws zoo ib yam li xoom lossis tsawg dua.
• Peb paub hais tias yog D> o, ib tug quadratic equation muaj tsuas yog ob tug sib txawv tiag tiag cov hauv paus hniav, lawv feem ntau sawv cev x ₁ thiab x _2,
  Ntawm no yog yuav ua li cas:
  x ₁ = (C + √D) :( 2a) thiab lub thib ob: x ₂ = (-to-√D) :( 2a).
• D = o yog ib lub hauv paus, los yog, lawv hais tias, ob leeg sib npaug:
  x ₁ yog sib npaug zos rau ₂ thiab yog sib npaug zos -to: (2a).
• Thaum kawg, D

Cia peb xav txog cov kev ua tsis tiav ntawm qib ob

1. taus ² + bx = o. Lub qhov sij hawm, coefficient c thaum x ⁰ yog sib npaug zos rau zero, ib tug ≠ o.
   Yuav ua li cas los daws kom tau qhov sib npaug quadratic tsis tiav ntawm hom no? Peb coj x rau cov nkhaus. Peb nco qab thaum qhov khoom ntawm ob yam tseem ceeb yog xoom.
   X (taus + b) = o, qhov no ua tau yog thaum x = 0 lossis thaum taus + b = o.
   Txiav txim siab 2nd linear kab zauv, peb muaj x = C / a.
   Raws li ib tug tshwm sim, peb muaj cov hauv paus hniav x ₁ = 0, Los ntawm cov lus teb x ₂ = -B / _a.
2. Tam sim no tus co ntawm qhov x yog sib npaug rau o, thiab c tsis sib npaug (≠) o.
   ² x + c = o. Yuav tsiv mus nyob rau sab xis ntawm lub kab zauv, peb tau txais x ² = c. Qhov zauv no tsuas muaj tseeb cov hauv paus hniav thaum -c yog tus nab npawb zoo (c x yog sib npaug zos rau ₁ yog hais tias √ (c), ntsig txog, x ₂ - -√ (c). Txwv tsis pub, cov kab zauv tsis muaj keeb kwm txhua.
3. Kev xaiv lub xeem: b = c = o, piv txwv li ² s = o. Lawm, zoo li qhov sib npaug yooj yim muaj ib tus cag, x = o.

Cov rooj plaub tshwj xeeb

Yuav ua li cas los daws qhov tsis tiav quadratic kab zauv, thiab tam sim no peb coj txhua yam.

• Hauv qhov kev ntsuas quadratic, qhov thib ob coefficient rau x yog tus lej txawm.
  Cia k = o, 5b. Peb muaj cov qauv rau xam cov kev ntxub ntxaug thiab cov hauv paus hniav.
  D / 4 ² = k - ac, keeb kwm xoo li x _{1,2 = (-k ± √ (D} / 4)) / a thaum D> o.
  X = -k / a rau D = o.
  Yog tsis muaj cov hauv paus hniav rau D
• Yog muab quadratic equations thaum lub coefficient ntawm x squared yog 1, lawv feem ntau yog sau x ² + p + q = o. Tag nrho cov saum toj no cov qauv siv rau lawv, cov lus teb yog me ntsis yooj yim.
  Piv txwv li ² x 9--4h = 0. laij D: 2 ² +9, D = 13.
  = X ₁ 2 + √13, x ₂ = 2-√13.
• Nyob rau hauv tas li ntawd, muab tau yooj yim thov lub theorem ntawm Vieta. Nws hais tias qhov sib npaug ntawm cov kab zauv yog -p, qhov thib ob coefficient nrog rho tawm kos npe (lub ntsiab lus ntawm cov lus sib li cas), thiab cov khoom ntawm tib cov hauv paus hniav sib npaug q, lub sij hawm dawb. Xyuas seb nws yooj yim npaum li cas yuav tsum tau los txiav txim seb lub hauv paus ntawm kab zauv no. Rau unreduced (rau tag nrho cov coefficients tsis sib npaug zos rau zero), qhov no theorem yog thov raws li nram no: lub sum x ₁ + x ₂ yog sib npaug zos -to / a, cov khoom x ₁ · x ₂ yog sib npaug zos rau ib tug / ib tug.

Qhov lej ntawm lub sij hawm pub dawb thiab cov thawj coefficient tus yog sib npaug zos rau cov coefficient b. Hauv qhov teeb meem no, cov kab zauv muaj tsawg kawg yog ib lub hauv paus (yooj yim los ua pov thawj), thawj zaug yuav tsum yog -1, thiab ob yuav tsum yog c / a, yog tias nws muaj. Yuav ua li cas los daws qhov kev ua tsis tiav quadratic, koj tuaj yeem tshawb xyuas koj tus kheej. Yooj yim dua yooj yim. Cov coefficients tuaj yeem ua qee qhov kev sib raug zoo ntawm lawv tus kheej

• x ² + x = o, 7x ² -7 = o.
• Tus lej ntawm tag nrho cov coefficients yog o.
  Cov hauv paus ntawm kab zauv no yog 1 thiab c / a. Piv txwv, 2 x 2 -15 x + 13 = o.
  ₁ = x 1, x ₂ = 13/2.

Muaj ntau txoj hauv kev los daws cov teeb meem sib txawv dua ob qib. Ntawm no, piv txwv li, yog txoj kev cais kev tawm tsam ntawm ib qho kev muab polynomial. Nws muaj ntau txoj kev zoo. Thaum koj nquag nrog cov piv txwv no, koj yuav kawm tau "nias" lawv zoo li cov noob, vim hais tias txhua txoj hauv kev yuav tau txais kev cia siab.