Nov yog kab lus yuav ua li cas ntsuas tus lej cuv npe. Peb yuav tshawb xyuas yuav ua li cas txhawm rau siv cov pab pawg zoo li siv cov xwm txheej los ntawm cov lus ywj pheej.
Kauj ruam
Txoj Kev 1 ntawm 2: Txheeb cais los ntawm Pawg
Kauj Ruam 1. Pab pawg polynomial ua ob ntu
Kev sib faib cov npe sib faib ua ob ntu yuav tso cai rau koj txhawm rau cais ib feem cais.
Piv txwv tias peb siv tus lej sib npaug: x3 + 3 x po2 - 6x - 18 = 0. Sib cais (x3 + 3 x po2) thiab (- 6x - 18).
Kauj Ruam 2. Nrhiav cov xwm txheej uas zoo ib yam hauv txhua ntu
- Los ntawm (x3 + 3 x po2), peb tuaj yeem pom qhov zoo ib yam yog x2.
- Los ntawm (- 6x - 18), peb tuaj yeem pom qhov sib npaug yog -6.
Kauj Ruam 3. Siv qhov sib npaug ntawm ob nqe lus
- Tshem tawm qhov x2 los ntawm thawj ntu, peb tau txais x2(x + 3).
- Siv qhov tseem ceeb -6 tawm ntawm ntu ob, peb tau -6 (x + 3).
Kauj Ruam 4. Yog tias txhua qhov ntawm ob nqe lus muaj tib yam, koj tuaj yeem ua ke sib koom ua ke
Koj yuav tau txais (x + 3) (x2 - 6).
Kauj Ruam 5. Nrhiav cov lus teb los ntawm kev saib cov hauv paus hniav ntawm kev ua zauv
Yog koj muaj x2 ntawm cov hauv paus hniav ntawm kab zauv, nco ntsoov tias ob tus lej zoo thiab tsis zoo yuav txaus siab rau qhov sib npaug.
Cov lus teb yog -3, 6 thiab -√6
Txoj Kev 2 ntawm 2: Txheeb Xyuas Siv Cov Lus Pub Dawb
Kauj Ruam 1. Npaj cov kab zauv rau hauv daim ntawv aX3+xwb2+txX+d.
Piv txwv tias peb siv tus lej sib npaug: x3 -4x ib2 -7x + 10 = 0
Kauj Ruam 2. Nrhiav txhua yam ntawm "d"
Qhov "d" tsis tu ncua yog tus lej uas tsis muaj qhov hloov pauv, xws li "x", nyob ib sab ntawm nws.
Cov lej yog cov lej uas tuaj yeem muab sib xyaw ua ke kom tau txais lwm tus lej. Hauv qhov no, qhov tseem ceeb ntawm 10, uas yog "d", yog: 1, 2, 5, thiab 10
Kauj Ruam 3. Nrhiav ib yam uas ua rau cov polynomial sib npaug rau xoom
Peb yuav tsum txiav txim siab yam twg ua rau cov lej sib npaug rau xoom thaum peb hloov cov lej rau txhua "x" hauv kab zauv.
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Pib nrog thawj qhov, uas yog 1. Hloov "1" rau txhua "x" hauv kab zauv:
(1)3 - 4(1)2 - 7(1) + 10 = 0.
- Koj yuav tau txais: 1 - 4 - 7 + 10 = 0.
- Txij li 0 = 0 yog nqe lus tseeb, koj paub tias x = 1 yog cov lus teb.
Kauj Ruam 4. Ua qee qhov chaw
Yog x = 1, koj tuaj yeem rov sau nqe lus kom nws zoo li txawv me ntsis yam tsis hloov nws lub ntsiab lus.
"x = 1" yog tib yam li "x - 1 = 0". Koj tsuas yog rho tawm "1" los ntawm txhua sab ntawm qhov sib npaug
Kauj Ruam 5. Siv lub hauv paus ntawm kev ua zauv los ntawm qhov seem ntawm qhov sib npaug
"(x - 1)" yog lub hauv paus ntawm qhov sib npaug. Txheeb xyuas yog tias koj tuaj yeem txheeb xyuas qhov seem ntawm qhov sib npaug. Tshem tawm cov polynomials ib tus zuj zus.
- Koj tuaj yeem txiav tawm (x - 1) los ntawm x3? Tsis yog Tab sis koj tuaj yeem qiv -x2 ntawm qhov sib txawv thib ob, tom qab ntawd koj tuaj yeem ntsuas nws: x2(x - 1) = x3 -x ib2.
- Koj puas tuaj yeem ntsuas (x - 1) ntawm qhov seem ntawm qhov sib txawv thib ob? Tsis yog Koj yuav tsum tau qiv me ntsis los ntawm qhov sib txawv thib peb. Koj yuav tsum tau qiv 3x los ntawm -7x. Qhov no yuav muab cov txiaj ntsig -3x (x -1) = -3x2 + 3 x po.
- Txij li thaum koj coj 3x los ntawm -7x, qhov sib txawv thib peb dhau los -10x thiab qhov tas li yog 10. Koj tuaj yeem ntsuas nws? Yog! -10 (x -1) = -10x + 10.
- Koj ua dab tsi yog teeb tsa qhov sib txawv kom koj tuaj yeem faib tawm (x - 1) los ntawm tag nrho cov kab zauv. Koj rov kho qhov sib npaug rau ib yam zoo li no: x3 -x ib2 -3x ib2 + 3x - 10x + 10 = 0, tab sis qhov sib npaug tseem sib npaug x3 -4x ib2 -7x + 10 = 0
Kauj Ruam 6. Txuas ntxiv nrog cov yam ntawm lub sijhawm ywj pheej
Saib tus lej uas koj tau siv (x - 1) hauv qib 5:
- x kev2(x - 1) - 3x (x - 1) - 10 (x - 1) = 0.2 -3x -10) = 0.
- Ntawm no, koj tsuas yog xav tau tus lej (x2 -3x10). Qhov tshwm sim ntawm kev cais yog (x + 2) (x - 5).
Kauj Ruam 7. Koj cov lus teb yog cov hauv paus keeb kwm ntawm qhov sib npaug
Koj tuaj yeem tshawb xyuas seb koj cov lus teb puas yog los ntawm kev ntsaws txhua lo lus teb, cais, rau hauv qhov kev ua zauv qub.
- (x - 1) (x + 2) (x - 5) = 0. Qhov no yuav muab cov lus teb 1, -2 thiab 5.
- Plug -2 rau qhov kev ua zauv: (-2)3 - 4(-2)2 - 7(-2) + 10 = -8 - 16 + 14 + 10 = 0.
- Plug 5 rau qhov kev ua zauv: (5)3 - 4(5)2 - 7(5) + 10 = 125 - 100 - 35 + 10 = 0.
Lub tswv yim
- Tsis muaj lub voos xwmfab polynomial uas tsis tuaj yeem suav nrog siv tus lej tiag vim tias txhua lub voos xwmfab ib txwm muaj lub hauv paus tiag. Cube polynomial zoo li x3 + x + 1 uas muaj lub hauv paus tiag tiag tsis muaj peev xwm tsis tuaj yeem muab coj los ua piv txwv nrog cov lej lossis cov lej sib npaug. Txawm hais tias nws tuaj yeem txiav txim siab los ntawm lub mis lub mis, nws tsis tuaj yeem raug txo los ua cov lej ntau ntxiv.
- Ib lub voos xwmfab polynomial yog cov khoom ntawm peb lub npe sib npaug rau lub zog ntawm ib lossis cov khoom lag luam ntawm cov npe sib npaug rau lub zog ntawm ib qho thiab cov lej sib npaug rau lub zog ntawm ob qho uas tsis tuaj yeem ua qhov tseeb. Rau cov xwm txheej zoo li tom kawg, koj siv sijhawm faib ntev tom qab nrhiav thawj lub zog polynomial kom tau txais lub zog thib ob polynomial.
