Koj puas tau hnov qab yuav ua li cas los daws qhov kev ua tsis tiav quadratic?

2024 Tus sau: Angel Austin | [email protected]. Kawg hloov kho: 2024-01-09 16:33

Yuav ua li cas los daws qhov tsis tiav quadratic equation? Nws yog lub npe hu hais tias nws yog ib tug tshwj xeeb version ntawm qhov sib npaug yuav yog xoom - ib txhij los yog nyias. Piv txwv li, c=o, v ≠ o los yog vice versa. Peb yuav luag nco qab lub ntsiab lus ntawm ib qho kev sib npaug plaub npaug.

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Lub trinomial ntawm qhov degree thib ob yog sib npaug rau xoom. Nws thawj coefficient a ≠ o, b thiab c tuaj yeem ua rau txhua tus nqi. Tus nqi ntawm qhov sib txawv x yuav yog lub hauv paus ntawm qhov sib npaug thaum, thaum hloov pauv, nws hloov mus rau qhov tseeb tus lej sib npaug. Cia peb nyob ntawm cov hauv paus hniav tiag tiag, txawm hais tias cov lej tsis sib xws kuj tuaj yeem daws qhov sib npaug. Nws yog kev cai hu rau ib qho kev ua kom tiav yog tias tsis muaj ib qho ntawm cov coefficients sib npaug rau o, tab sis ≠ o, rau ≠ o, c ≠ o.

daws qhov piv txwv. 2x²-9x-5=oh, we find

D=81+40=121, D yog qhov zoo, yog li muaj cov hauv paus, x1 _{=(9+ √121): 4=5 thiab qhov thib ob x}2 _{=(9-√121): 4=-o, 5. yuav pab kom lawv paub tseeb.}

Ntawm no yog ib kauj ruam los ntawm kev daws teeb meem rau plaub qhov sib npaug

Los ntawm qhov kev ntxub ntxaug, koj tuaj yeem daws qhov sib npaug, nyob rau sab laug uas muaj lub npe square trinomial nrog ≠ o. Hauv peb qhov piv txwv. 2x²-9x-5=0 (ax^2+in+s=o)

• Ua ntej, nrhiav tus neeg ntxub ntxaug D siv cov qauv paub hauv 2-4ac.
• Kuaj seb tus nqi D yuav yog li cas: peb muaj ntau tshaj xoom, nws tuaj yeem sib npaug rau xoom lossis tsawg dua.

• Peb paub tias yog D › o, qhov sib npaug plaub npaug tsuas muaj 2 lub hauv paus tiag tiag, lawv txhais tau tias x₁ feem ntau thiab x₂, qhov no yog li cas nws suav:

  x₁=(-v + √D): (2a), thiab qhov thib ob: x _{2=(-in-√D):(2a).}

• D=o - ib cag, los yog, lawv hais, ob qhov sib npaug:

  x ₁ sib npaug rau x_{2 thiab sib npaug -v:(2a).}

• Thaum kawg, D ‹ o txhais tau tias qhov sib npaug tsis muaj cov hauv paus tiag tiag.

Cia peb xav txog dab tsi yog qhov sib npaug tsis tiav ntawm qib thib ob

1. ax²+in=o. Lub sij hawm pub dawb, tus coefficient c ntawm x⁰, yog xoom ntawm no, ntawm ≠ o.

   Yuav ua li cas los daws qhov tsis tiav quadratic equation ntawm hom no? Wb coj x tawm ntawm cov hlua. Nco ntsoov thaum cov khoom ntawm ob yam yog xoom.

   x(ax+b)=o, qhov no tuaj yeem yog thaum x=o lossis thaum ax + b=o.

   Txoj kab zauv thib 2;

   x₂ =-b/a.

2. Tam sim no tus coefficient ntawm x yog o thiab c tsis sib npaug (≠)o.

   x²+s=o. Wb mus rau sab xis ntawm kev sib npaug, peb tau x² =-с. Qhov kev sib npaug no tsuas muaj cov hauv paus tiag tiag thaum -c yog tus lej zoo (c ‹ o), x ₁ ces sib npaug √(-c), feem x _{2 ― -√(-s). Txwv tsis pub, qhov sib npaug tsis muaj cov hauv paus ntsiab lus.}

3. Kev xaiv kawg: b=c=o, i.e. ah2=o. Lawm, xws li ib tug yooj yim kab zauv muaj ib lub hauv paus, x=o.

Special case

Yuav ua li cas los daws qhov kev sib npaug plaub npaug tsis tiav tau txiav txim siab, thiab tam sim no peb yuav ua txhua yam.

Nyob rau hauv qhov kev sib npaug tag nrho, qhov coefficient thib ob ntawm x yog tus lej sib npaug.

Cia k=o, 5b. Peb muaj cov qauv rau kev suav cov kev cais thiab cov hauv paus hniav.

D/4=k²-ac, cov hauv paus hniav raug suav raws li qhov no x _{1, 2=(-k±√(D/4))/a rau D › o.}x=-k/a rau D=o.

No cag rau D ‹ o.

Tseem txo qis qhov sib npaug, thaum coefficient ntawm x squared yog 1, feem ntau lawv sau x² +px+ q=o. Tag nrho cov qauv saum toj no siv rau lawv, tab sis cov kev suav yog me ntsis yooj yim dua. 2

=2-√13.

Dhau li ntawd, Vieta lub theorem tuaj yeem siv tau yooj yim rau cov uas tau muab. Nws hais tias qhov sib npaug ntawm cov hauv paus hniav ntawm qhov sib npaug yog -p, qhov thib ob coefficient nrog tus rho tawm (lub ntsiab lus ntawm cov cim qhia tawm), thiab cov khoom ntawm tib cov hauv paus hniav yuav sib npaug rau q, lub sij hawm pub dawb. Xyuas seb yuav ua li casnws yuav yooj yim rau kev hais lus txiav txim siab cov hauv paus hniav ntawm qhov sib npaug no. Rau qhov tsis txo qis (rau txhua qhov tsis yog xoom coefficients), qhov theorem no siv tau raws li hauv qab no: 1x₂ equal to/a.

Cov lej ntawm lub sijhawm pub dawb c thiab thawj coefficient a yog sib npaug rau cov coefficient b. Hauv qhov xwm txheej no, qhov sib npaug muaj tsawg kawg yog ib lub hauv paus (nws yog ib qho yooj yim los ua pov thawj), thawj tus yuav tsum sib npaug rau -1, thiab qhov thib ob - c / a, yog tias muaj. Yuav ua li cas los daws qhov kev ua tsis tiav plaub fab, koj tuaj yeem tshawb xyuas koj tus kheej. Yooj yim npaum li lub ncuav qab zib. Coefficients tuaj yeem nyob hauv qee qhov piv ntawm lawv tus kheej

• x²+x=o, 7x^2-7=o.

• Cov sum ntawm tag nrho cov coefficients yog o.

  Cov hauv paus hniav ntawm qhov sib npaug yog 1 thiab c/a. Piv txwv, 2x²-15x+13=o.

  x₁ =1, x_2=13/2.

Muaj ntau txoj hauv kev los daws qhov sib npaug sib txawv ntawm qib thib ob. Ntawm no, piv txwv li, yog ib txoj hauv kev rau rho tawm tag nrho cov square los ntawm ib tug muab polynomial. Muaj ntau txoj hauv kev nraaj. Thaum koj feem ntau cuam tshuam nrog cov piv txwv zoo li no, koj yuav kawm "nias" lawv zoo li cov noob, vim tias txhua txoj hauv kev tuaj yeem nkag siab.