
beejaganita padaprayogam

ganithashaasthrathil, sthiramaaya beejaganita samkhyakal, variableukal, beejaganita pravartthanangal (koottal, kuraykkuka, gunanam, vibhajanam, ghaathaamkam, yukthisahamaya samkhya) ennivayil ninnu nirmmicha oru padaprayogamaanu beejaganita padaprayogam. udaaharanathinu, ithu oru beejaganita padaprayogamaanu. square root edukkunnathu pavarilekku uyarthunnathinu thulyamayathinaal, inipparayunnavayum oru beejaganita padaprayogamaanu
beejaganita padaprayogangal maathram ulppedunna oru samavaakyamaan "beejaganita samavaakyam".
ithinu vipareethamaayi, divyasankhyakal poornnasamkhyaasampradaayil ninnum beejaganita pravarthanangalil ninnum uruthirinjathallaathinal avaa beejaganithamallaathavayaanu. saadhaaranayaayi, oru jyaamitheeya bandhamaayi nirmmikkappedunnu, athinte nirvachanathinu beejaganita pravartthanangalude "ananthamaaya ennam" aavasyamaanu.
ganithashaasthra pravartthanangalude gunangal (koottalinteyum gunanathinteyum commutative gunangalum associative gunangalum, vitharana gunavum bhinnasamkhyakalile pravartthanangalude niyamangalum) upayogichu yukthisahamaya bhinnasamkhyayilekku maattiyezhuthaavunna oru padaprayogamaanu yukthisahamaya padaprayogam. mattoru vidhathil paranjaal, ganithatthinte naalu pravartthanangal maathram upayogichu veriyabilukalil ninnum sthiraangangalil ninnum nirmikkaavunna oru padaprayogamaanu yukthisahamaya padaprayogam. athinaal, 
yukthisahamaya oru padaprayogamaanu, athesamayam 
illa.
yukthisahamaya samavaakyam ennathu roopathinte rund yukthisahamaya bhinnasamkhyakal (allengil yukthisahamaya padaprayogangal) ulla oru samavaakyamaan. 
avaa parasparam thulyamaayi sajjeekarichirikkunnu. eee padaprayogangal bhinnasamkhyakalude athe niyamangal anusarikkunnu. cross-multiply cheiyunnathiloode samavaakyangal pariharikkanaakum. poojyathaal vibhajikkunnath nirvachikkappedaathathinaal poojyathaal aupachaarikamaayi vibhajikkunna oru pariharam nirasikkappedunnu.
padavali.
oru padaprayogatthinte bhagangal vivarikkan beejaganithathinu athintethaaya padaavaliyunda
<bii. aarr.>
1-eksponant (power), 2-coffificient, 3-tame, 4-oopparettar, 5-konsttant, formula _ 5-variableukal
polynomialukalude verukalil.
n" <5 aanenkil digri "n" enna polynomial eksprashante verukal allengil thathulyamaaya oru polynomial samavaakyathinte pariharangal ellaayppozhum beejaganita expressionukalaayi ezhuthaam (quadratic formula, cubic function, quartic samavaakyam enniva kaanuka). oru samavaakyathinte atharamoru parihaarathe beejaganita pariharam ennu vilikkunnu. ennaal "n" soothravaakyam _ 65 aanenkil atharam ellah samavakyangalkkum (avayil chilathinu maathram) beejaganita pariharangal nilavilillenn abel-rufini sidhaantham prasthaavikkunnu.
kanvenshanukal.
variableukal.
parambaraagathamaayi, aksharamaalayude thudakkathile aksharangal (udha.jii. formula _ 7) saadhaaranayaayi sthiraangangale prathinideekarikkaan upayogikkunnu, koodaathe aksharamaalayude avasaanabhaagathullava (iii.jii. formula _ 5 umm formula _ 9 umm variabilukale prathinideekarikkaan upayogikkunnu. avaa saadhaaranayaayi itaalik bhaashayilaan ezhuthappedunnathu.
exponentukal.
parambaraagathamaayi, ettavum uyarnna shakthiyulla (eksponant) padangal idathuvashathu ezhuthappedunnu, udaaharanathinu, formula _ 10 formula _ 11-nte idathuvashathu ezhuthunnu. oru coffificient onnaayirikkumbol, athu saadhaaranayaayi ozhivaakkappedunnu (iii.jii. formula _ 12 ennathu formula _ 10) ennaanu ezhuthiyirikkunnathu. athupole ghaathaamkam (shakti) onnaayirikkumbol, (iii.jii. formula _ 14 ennathu formula _ 15) ennu ezhuthappettirikkunnu, eksponant poojyamaakumbol phalam ellaayppozhum 1 (e.jii. formula _ 16 ennathu formula _ 17 ennu ezhuthappettirikkunnu, kaaranam formula _ 18 ellaayppozhum formula _ 19 aanu).
beejaganithavum mattu ganitha padaprayogangalum.
pothuvayathum ennaal saarvathrikavumaaya kanvenshanukalkkanusrithamaayi allatha gadakangalude tharam anusarichu beejaganita padaprayogangal mattu pala tharatthilulla ganitha padaprayogangalumaayi engane thaarathamyam cheiyunnuvennu chuvadeyulla pattika samgrahikkunnu.
yukthisahamaya beejaganita padaprayogam" (allengil "yukthisahamaya padaprayogam") ennathu polynomialukalude oru bhaagamaayi ezhuthaan kazhiyunna oru beejaganita padaprayogamaanu, udaaharanathinu. yukthirahithamaya beejaganita padaprayogam yukthirahithamaan, udaaharanathinu.