Wamakelekile kwintetho echaza indlela yokusebenzisa i"quadratic equation".

Ngoko ke i"quadratic equation". ivakala ngathi yinto

enobunzima kakhulu.

Kwaye xa uqala ukubona i"quadratic equation, ungathi

kulungile, hayi ukuphela ivakala njengento

enobunzima, kodwa yinto enzima.

Kodwa ngethemba uakubona, njengokuba sisaqubekeka

nentetho yethu, ukuba ayikhonzima ukuyisebenzisa.

Kwaye kwintetho ezayo exesheni ndizakubonisa

indlela eyakhiwe ngayo.

Ngoko ke, jikelele, sowufundile ukwenza ucalu calulo

kwiqondo lesibini lalonxaki.

Ufundile ukuba, ukuba ndino, mandithi "x" ophinda-phindwe kabini thabatha

"x" thabatha 6, ilingana no0.

Ukuba bendinalenxaki. "x" ophinda-phindwe kabini thabatha "x" thabtha "x' ilingana

no0, lanto ungayicalu calulala uthi "x" thabatha 3 kwaye

"x" dibanisa 2 ilingana no0.

Ngokucacileyo ithetha ukuba "x" thabatha 3 lingana no 0 okanye

"x" dibanis 2 lingana no0.

Ngoko ke "x" thabatha 3 lingana no0 okanye "x' dibanisa 2 lingana no0.

Ngoko ke "x" lingana no 3 okanye no thabatha 2.

Kwaye, xa siyizoba phantsi yalento izakuba, ukuba bendino

msebenzi othile "f" ka "x" ulingana no "x" ophinda-phindwe kabnini thabatha "x' thabatha 6.

Ngoko ke lomgca usembindini ngoka "f" ka "x".

Ungaqhelana kakhulu nomgca osembindini we"y".

kulenxaki inje, akukho nxaki khakhulu.

Kwaye lomgca usembindini we "x".

Kwaye ukuba bekuzakufuneka ndiyizobile lenxaki, "x' ophinda-phindwe kabini thabatha "x"

thabatha 6, ingajongeka ngoluhlobo.

Kancinci ngoluhlobo--lento ngu "f' ka "x" ulingana no thabatha 6.

Kwaye umfanekiso ozotyiweyo angakhangeleka ngolu hlobo.

Nyuka, izakuhlala inyuka ngokwalandlela.

Kwaye ngoku iya kuthabatha 6, ngoba xa "x' elingana no0.

'F" ka 'x" ulingana no thabatha 6.

Ngoko ke ndiyayazi iyagqitha pha kulancam.

kwaye ndiyayazi ukuba xa "f' ka 'x' elingana no0, ngoko ke 'f' ka 'x' lingana

no 0 ngaphezu komgca osembindini ka 'x', akunjalo?

Ngoba lento ngu1.

lento ngu0.

lento ngu thabatha 1.

Ngoko ke lento ngu, xa 'f' ka 'x' elingana no0, ngaphezulu

komgca osembindini ka 'x', akunjalo?

Kwaye siyayazi ilingana no0 kula ncam 'x' lingana no 3 kwaye

'x' lingana no thabatha 2.

Yeyonanto isiyicombululeyo apha.

Mhlawumbi xeshikweni besisenza inxaki yokucazulula khange

siqwalasele ngokomzobo wethu into besiyenza.

Kodwa ukuba sithi la 'f' ka 'x' ulingana nenaki ethile, sayi

lungiselela lanto yalingana no0.

Ngoko ke sithi lenxaki, kuphi apho

ilingana no0?

Xa kutheni ilingana no0?

Kulungile, ilingana no0 kwincam, akunjalo/

Ngoba kulapho u'f' ka 'x' elingana no0.

Kwaye kwangoko into besiyenza xa besisombulula lento ngoku

cazulula ku, sibonile ukuba, iinxnye zika'x' ezenze u 'f' ka 'x'

lingana no0, ngokucacileyo ngezi ncam zimbini.

Kwaye, ngokwe sigama, ezi zibizwa

ngamaqanda, okanye ingcambu, zika 'f' ka 'x'.

Makhe siqwalase lanto kancinane.

Ngoko ke , ukuba ndinento enje ngo'f' ka 'x' ulingana no'x' ophinda-phindwe kabini dibanisa

'4x' dibanisa 4, kwaye ndibuze kuwe, aphi amaqanda okanye

ingcambu zika 'f' ka'x'.

Yinto enye nokuthi, kuphi apho u'f' ka 'x'

adinana khona nomngca osembindini ka'x'.

Kwaye badibana xa umgca osembindika ka'x' 'f' ka 'x' eli

ngana no0, akunjalo?

Ukuba uyacinga ngomzobo bendikhe ndawenza we'graph'.

Ngoko ke, masithi ukuba u 'x' ulingana no 0, kwangoko

singathi, 0 ulingana no'x' ophinda-phindwe kabini dibanisa '4x' dibanisa 4.

Kwaye siyayazi, singazicalu calula, ngu 'x'

dibanisa 2 phinda-phinda 'x' dibanisa 2.

Kwaye siyayazi ukuba iyalingana no0 xa 'x' elingana no thabatha 2.

'x' ulingana no thabatha 2.

Kulungile, kancinci--'x' ulingana no thabatha 2.

Ngoko ke ngoku, siyayazi singamfumana njani u0 xa eyona

nxaki kulula ukuyicazulula.

Kodwa masenze eyona nxaki apho inxaki yethu

kungakho lula ukuyicazulula konke konke.

Masithi sino 'f' ka 'x' ulingana nothabatha '10x'

ophinda-phindiweyo kabini thabatha '9x' dibanisa 1.

Kulungile, xa ndijonga lento, nokuba bendino kuyahlula ngo 10 bendino

nokufumana amaqhezu apha.

Kwaye kunzima ukuyicinga indlela yokucazulula lento i'quadratic'

Kwaye yilonto ibizwa ngokuba yi"quadratic equation" okanye

liqondo lesibini lamanani anezalathi ezinga phezu kwesithathu.

Kodwa masiyicwangcise-- Ngoko ke sizama ukuyisombulula lento.

Ngoba sifuna ukuyazi kuphi xa ilingana no0.

Thaba '10x' ophonda-phindwe kabini thabatha '9x' dibanisa 1.

Sifuna ukwazi ngawaphi lamanani asendaweni ka'x' enza lento

ilingane no0.

Kwaye apha singasebenzisa isixhobo esibizwa ngokuba yi"quadratic equation".

Kwaye ngoku ndizakuninika enye kezinqabileyo kwizibalo

kwaye ngumbono omhle ukuyigcina enqondweni.

I"quadratic equation' ithi ingcambu ze"quadratic'

ziyalingana--kwaye masithi i'quadratic equation' ngu

'x' mophinda-phindwe kabini dibanisa 'bx' dibanisa 'c' lingana no0.

Ngoko ke kulomzekelo, u'a' ngu thabatha 10.

'b' ngu thabatha 9, kwaye 'c' ngu 1.

Isichazi se"quadratic fomula' yi ngcambu ka 'x' ilingana no thabatha 'b' dibanisa okanye thabatha

ingcambu ephinda-phindwa kabini ka'b' thabatha u 4 phinda-phinda 'a' phinda-phinda 'c',

yonke lonto ngaphezu ko' 2a'.

Ndiyayazi ukuba ijongenga nzima kodwa xa uyisebenzisa ngamandla, uzakubona

ukuba ayikhombi kwaphela.

Kwaye ngumbono omhle ukuyi bamba ngengqondo.

Ngoko ke masibandakanye i"quadratic ewauation' apha kulenxaki

sisandula ukuyibhala phantsi.

Ngoko ke ndithi sandula ukuthi--kwaye jonga, kukho into ecaleni

kuka 'x', akunjalo?

'a' ngumlingani ka 'x' ophinda-phindiweyo.

'b' ngumlingani ka 'x' kwaye u'c' akatshintshi.

Ngoko ke masiyisebenzise kule nxaki.

Ngubani u-'b'?

Kulungile, 'b' ngu thabatha 9.

Singabona apha.

'b' nguthabatha 9, 'a' ngu thabatha 10.

'c' ngu 1.

Akunjalo?

Ngoko ke ukuba u-'b' ngu thabatha 9--ngoko ke masithi, nguthabatha 9.

Dibanisa okanye thabatha ingcambu kathabatha 9 ophinda-phindwe kabini.

Kulungile, ngu 81.

thabatha 4 phinda-phinda ngo 'a'

'a' ngu thabatha 10.

Thabatha 10 phinda-phinda 'c', ngokucacileyo ngu 1.

Ndiyayazi lento ithesa, kodwa ngethemba uza

kuyiqonda.

kwaye yonke lonto ngaphezu ko2 umphinda-phinde ngo 'a'.

Kulungile, 'a' ngu thabatha 10, ngoko ke 2 phinda-phinda 'a' ngu thabahta 20.

Ngoko ke masiyicazulule lanto.

Thabatha 10 phinda-phinda ngo thabatha 6, ngu dibanisa 9.

Dibanisa okanye thabatha ingcambu ka 81.

Sino thabatha 4 umphinda-phinda ngo thabatha 10.

Lento ngu thabatha 10.

Ndiyayazi ithesa kakhulu, ndiyaxolisa kakhulu

ngalonto, phinda-phinda ngo 1.

ngoko ke thabatha 4 uphinda-phinde ngo thabatha 10 ngu 40, onesichazi esingu dibanisa 40.

Dibanisa 40.

Kwaye kwangoko sinazo zonke phezu ko thabatha 20.

Kulungile, 81 dibanisa 40 ngu 121.

Ngoko ke lento ngu 9 dibanisa okanye thabatha ingcambu

ka 121 phezu ko thabatha 20.

Ingcambu ka 121 ngu 11.

Ngoko ke ndizohamba apha.

Ngethemba awuzose uyiphose indlela yalento ndiyenzayo.

Ngoko ke lento ngu 9 dibanisa oakanye thabatha 11, ngaphezu ko thabatha 20.

kwaye ngoko ke ukuba sithi 9 dibanisa 11 phezu ko thabatha 20, ngu 9

dibanisa 11 ngu 20, ngoko ke lenti ngu 20 phezu ko thabatha 20.

Ngoku cacileyo ulingana no thabatha 1.

Ngoko ke yigcambu enye.

Ngu 9 dibanisa--ngoba lento ngu dibanisa oaknye thabatha.

Kwaye enye ingcambu izakuba ngu 9 thabatha 11 phezu ko thabatha 20.

Ngokucacileyo ilingana no thabatha 2 phezu ko thabatha 20.

ngokucacileyo ilingana no 1 phezu ko 10.

ngoko ke ngenye ingcambu.

Ngoko ke ukuba bekunokufuneka ziyizobe phantsi lenxaki, besizokubona ukuba

ngokucacileyo idibana kumgca osembindini ka'x',

Okanye 'f' ka 'x' ulingana no0 kwincam ka'x' elingana no thabatha

1 kwaye 'x' ulingana no 1/10.

Ndizakwenza imizekelo eminizni kwicandelo lesibini, ngoba ndi

yacinga, ukuba nantoni na, ndingani bhidekisa

ngalena yodwa.

ngoko ke, ndizakunibona kwicandelo lesibini sisebenzisa

"quadratic equation".