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EIPB\

"eikasbfueirpbysals.ak" 9

Yui`rital Mquitagk

9. ^ghykgeaih :I oukltag k o `moakm` dy o(x ) 5 i

kxk + i

k 9xk 9 + .......+ i

9x + i

>

wbmrm i>, i

9, i

4, ......, i

k T as lihhm` i pghykgeaih go `mcrmm k watb rmih lgmooalamkts (i

k >, k S ).

Ao i>, i

9, i

4, ....., i

k L, at as lihhm` i pghykgeaih watb lgephmx lgmooalamkts.

4. Yui`rital pghykgeaih Yui`rital mquitagk :I pghykgeaih go `mcrmm 4 as fkgwk is qui`rital pghykgeaih. Iky mquitagk o(x) 5 >, wbmrm o as i qui`rital

pghykgeaih, as lihhm` i qui`rital mquitagk. Pbm cmkmrih ogre go i qui`rital mquitagk as

ix4 + dx + l 5 > .......(a)

Sbmrm i, d, l irm rmih kuedmrs, i >.

Ao i 5 >, tbmk mquitagk (a) dmlgems hakmir mquitagk.

Gkm Tggt

i lgktri` altagk ao i 5 d 5 >, l > Kg Tggt

ik a`mktaty ao i 5 d 5 l 5 > Akoakatm Tggts

Ao ix4 + dx + l 5 > as sitasoam` dy tbrmm `astaklt vihums go ' x ', tbmk at as ik a`mktaty.

Mxiephm # 9 : (a) as i qui`rital mquitagk bmrm i 5 , x 5 9 ik` x 5 9 ik` bmklm at as ik a`mktaty dmliusm i pghykgeaih mquitagk go k tb

`mcrmm likkgt bivm egrm tbik k `astaklt rggts.

0 . Tmhitagk Dmtwmmk Tggts Lg-mooalamkts:(a) Pbm sghutagks go qui`rital mquitagk, i x4 + d x + l 5 >, (i >) as cavmk dy

x 5i4

li0dd 4

Pbm mxprmssagk, d4 0 i l@ as lihhm` `aslraeakikt go qui`rital mquitagk.(aa) Ao ,irm tbm rggts go qui`rital mquitagk,

i x4 + d x + l 5 > .......(a)

tbmk mquitagk (a) lik dm wrattmk is

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EIPB\

"eikasbfueirpbysals.ak" 4

i(x ) (x ) 5 >

gr ix4 i(+ )x + i 5 > ......(aa)

mquitagks (a) ik` (aa) irm a`mktalih,

dy lgepirakc tbm lgmooalamkts

sue go tbm rggts, + 5 i

d5

4xgotlgmooalamk

xgotlgmooalamk

ik` prg`ult go tbm rggts, 5i

l5 4xgotlgmooalamk

tmrettiklgks

(aaa) @ava`akc tbm mquitagk (a) dy i,

x4 +i

dx +

i

l5 >

x4

i

dx +

i

l5 >

x4 (+ )x + 5 >

x4 (sue go tbm rggts) x + (prg`ul t go tbm rggts) 5 >

Bmklm wm lgklhu`m tbit tbm qui`rital mquitagk wbgsm rggts irm & as x4 (+)x + 5 >

Mxiephm # 4 : Ao ik` irm tbm rggts go ix 4 + dx + l 5 >, oak` tbm mquitagk wbgsm rggts irm+4 ik`+4.

\ghutagk : Tmphilakc x dy x 4 ak tbm cavmk mquitagk, tbm rmquarm` mquitagk as

i(x 4)4 + d(x 4) + l 5 > a.m., ix4 (0i d)x + (0i 4d + l) 5 >.

Mxiephm # < : Pbm lgmooalamkt go x ak tbm qui`rital mquitagk x4 + px + q 5 > wis tifmk is 93 ak philm go 9, tbmk oak` tbm qui`rital mquitagk

wbgsm rggts irm

(a) 4, 4 (aa) 4

,4

(aaa) + 9, + 9

(av)

9

9,

9

9(v)

,

(4) Ao r dm tbm ritag go tbm rggts go tbm mquitagk ix4 + dx + l 5 >, sbgw tbitr

)9r( 45

il

d4

.

Ikswmrs : (9) (a) ix4 + 4dx + 0l 5 > (aa) i4x4 + (4il d4) x + l4 5 >

(aaa) ix4 (4i d) x + i + l d 5 >

(av) ( i + d + l)x4 4(i l) x + i d + l 5 >

(v) il x4

(d4

4il) x + il 5 >

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EIPB\

"eikasbfueirpbysals.ak" bivakc, is ats rggts6

@ d 4 0 i l

@ 5 > @ >Tggts irm mquih a.m. 5 5 d/4i Tggts irm ukmquih& tbm qui`rital mxprmssagk lik dm mxprmssm`

is i pmromlt squirm go i hakmir pghykgeaih

i, d, l T & @ ; > i, d, l T & @ 8 >Tggts irm rmih Tggts irm aeicakiry 5 p + a q, 5 p a q

i, d, l Y & i, d, l Y &@ as squirm go i ritagkih kue dmr @ as kgt squirm go i ritagkih kue dmr

Tggts irm ritagkih Tggts irm arritagkih

a.m. 5 p + q , 5 p q

i 5 9, d, l & @ as squirm go ik aktmcmr Tggts irm aktmcrih.

Mxiephm # 0 : Ogr wbit vihums go e tbm mquitagk (9 + e) x4 4(9 + bis mqui h rggts.

\ghutagk : Cavmk mquitagk as (9 + e) x4 4(9 + ... ... ..( a)

Hmt @ dm tbm `aslraeakikt go mquitagk (a).Tggts go mquitagk (a) wahh dm mquih ao @ 5 >.

gr 0(9 +

gr 0(9 + 1e4 + ?e 9 1e 2e4) 5 >

gr e4 gr, e(e

e 5 >, ) + 9 5 > bis

aktmcrih rggts.

\ghutagk : Bmrm tbm mquitagk as x4 (i + 9>)x + 9>i + 9 5 >. \akl m aktmcrih rggts wahh ihwiys dm ritagkih at

emiks @ sbguh` dm i pmromlt squirm.Orge (a) @ 5 i4 4>i + 1?.

@ 5 (i 9>)4 0 0 5 (i 9>)4 @Ao @ as i pmromlt squirm at emiks wm wikt `aoomrmklm go twg pmromlt squirm is 0 wbalb as pgssadhm

gkhy wbmk (i 9>)4 5 0 ik` @ 5 >.

(i 9>) 5 4 i 5 94, 2

Mxiephm # ? : Ao tbm rggts go tbm mquitagk (x i) (x d) f 5 > dm l ik` `, tbmk prgvm tbit tbm rggts go tbm

mquitagk (x l) (x `) + f 5 >, irm i ik` d.

\ghutagk : Dy cavmk lgk`atagk

(x i) (x d) f (x l) (x `)gr (x l) (x `) + f (x i) (x d)Idgv m sbgws tbit tbm rggts go (x l) (x `) + f 5 > irm i ik` d.

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"eikasbfueirpbysals.ak" 0

Mxiephm # 3 : @mtmreakm 'i' sulb tbit x4 99x + i ik` x4 90x + 4i eiy bivm i lgeegk oil tgr.

\ghutagk : Hmt x dm i lgeegk oiltgr go x 4 99x + i ik` x4 90x + 4i.Pbmk x 5 wahh sitasoy tbm mquitagks x4 99x + i 5 > ik` x4 90x + 4i 5 >.

4 99+ i 5 > ik` 4 90+ 4i 5 >\ghvakc (a) ik` (aa) dy lrgss euhtaphalitagk emtbg`, wm cmt i 5 >, 40.

Mxiephm # 2 : \bgw tbit tbm mxprmssagk x4

+ 4(i + d + l)x +

gr (i + d + l)4

gr4

9((i d)4 + (d l)4 + (l i)4) 5 >

wbalb as pgssadhm gkhy wbmk i 5 d 5 l.

\mho priltalm prgdhmes :

( ( T) dm i qui`rital mquitagk. Oak` tbm vihums go '' ogr wbalb(a) Dgtb rggts irm rmih ik` `astaklt.

(aa) Dgtb rggts irm mquih.(aaa) Dgtb rggts irm aeicakiry

(av) Dgtb rggts irm gppgsatm ak sack.

(v) Dgtb rggts irm mquih ak eickatu`m dut gppgsatm ak sack.

(3) Ao ^(x) 5 ix4 + dx + l, ik` Y(x) 5 ix 4 + `x + l, il > tbmk prgvm tbit ^(x) . Y(x) 5 > bisithmist twg rmih rggts.

Ikswmrs. (, & c(x) 5 > irm twg pghykgeaih mquitagk bivakc sgem lgeegk rggt(s) tbmk tbgsm lgeegk

rggt(s) as/irm ihsg tbm rggt(s) go b(x) i o(x) + dc (x) 5 >.

Mxiephm # 1 : Ao x4 ix + d 5 > ik` x4 px + q 5 > bivm i r ggt ak lgeegk ik` tbm smlgk` mquitagk bis mquih

rggts, sbgw tbit d + q 5 4

ip

.\ghutagk : Cavmk mquitagks irm : x4 ix + d5 > ... ..... (a)

ik` x4 px + q 5 >. ... .... . (aa)

Hmtdm tbm lgeegk rggt. Pbmk rggts go mquitagk (aa) wahh dmik`. Hmtdm tbm gtbmr rggt gomquitagk (a). Pbus rggts go mquitagk (a) irm, ik` tbgsm go mquitagk (aa) irm,.

Kgw + 5 i ........ (aaa) 5 d ........ (av)45 p ........ (v)4 5 q ........ (va)H.B.\. 5 d + q 5 +4 5(+) ........ (vaa)

ik` T.B.\. 54

ip5

4

4)( 5 ( + ) ........ (vaaa)

orge (vaa) ik` (vaaa), H.B.\. 5 T.B.\.

Mxiephm#9> : Ao i, d, lT ik` mquitagks ix4 + dx + l 5 > ik` x4 + 4x + 1 5 > bivm i lgeegk rggt, sbgw tbiti : d : l 5 9 : 4 : 1.

\ghutagk : Cavmk mquitagks irm : x4 + 4x + 1 5 > ........(a)

ik` ix4 + dx + l 5 > ........(aa)

Lhmirhy rggts go mquitagk (a) irm aeicakiry saklm mquitagk (a) ik` (aa) bivm i lgeegk rggt,

tbmrmogrm lgeegk rggt eust dm aeicakiry ik` bmklm dgtb rggts wahh dm lgeegk.

Pbmrmogrm mquitagks (a) ik` (aa) irm a`mktalih

9

i5

4

d5

1

l

i : d : l 5 9 : 4 : 1

\mho priltalm prgdhmes :

(2) A o tbm mquitagk x4 + dx + il 5 > ik` x4 + lx + id 5 > bivm i lgeegk rggt tbmk prgvm tbit tbm

mquitagk lgktiakakc gtbmr rggts wahh dm cavmk dy x 4 + ix + dl 5 >.

(1) Ao tbm mquitagks ix4 + dx + l 5 > ik` x< + ) Ao ix4 + 4dx + l 5 > ik` i9x4 + 4d

9x + l

95 > bivm i lgeegk rggt ik`

9i

i,

9d

d,

9l

lirm ak I.^..

sbgw tbit i9, d

9, l

9irm ak C.^.

3. Cripb go Yui`rital Mxprmssagk:y 5 o (x) 5 i x4 + d x + l

gr

i0

@y 5 i

4

i4

dx

tbm cripb dmtwmmk x, y as ihwiys i piridghi.

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EIPB\

"eikasbfueirpbysals.ak" ?

tbm lggr`akitm go vmrtmx irm

i0

@,

i4

d

Ao i ; > tbmk tbm sbipm go tbm piridghi as lgklivm upwir`s & ao i 8 > tbmk tbm sbipm go tbm

piridghi as lgklivm `gwkwir`s.

tbm piridghi aktmrsmlt tbm yixas it pgakt (>, l).

tbm xlggr`akitm go pgakt go aktmrsmltagk go piridghi watb xixas irm tbm rmih rggts go tbmqui`rital mquitagk o (x) 5 >. Bmklm tbm piridghi eiy gr eiy kgt aktmrsmlt tbm xixas.

2. Tikcm go Yui`rital Mxprmssagk o x) 5 ix4 + dx + l.(a) Tikcm :

Ao i ; > o (x)

,

i0

@

Ao i 8 > o (x)

i0

@,

Bmklm eixaeue ik` eakaeue vihums go tbm mxprmssagk o (x) as i0

@ak rmspmltavm lisms ik`

at gllurs it x 5i4

d(it vmrtmx).

(aa) Tikcm ak rms tr al tm` `gei ak :Cavmk x Vx

9, x

4U

(i) Ao i4

dVx

9, x

4U tbmk,

o (x) )}Ux(o),x(o{eix,)}x(o),x(o{eakV 4949

(d) Ao i4

dVx

9, x

4U tbmk,

o (x)

i0

@,xo,xoeix,

i0

@,xo,xoeak )()()()( 4949

Mxiephm# 99 : Ao l 8 > ik` ix 4 + dx + l 5 > `gms kgt bivm iky rmih rggts tbmk prgvm tbit

(a) i d + l 8 > (aa) 1i + .

\ghutagk : l 8 > ik` @ 8 > o(x) 5 ix4 + dx + l 8 > ogr ihh x T o( 9) 5 i d + l 8 >

ik` o(

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EIPB\

"eikasbfueirpbysals.ak" 3

Mxiephm# 94: Oak` tbm eixaeue ik` eakaeue vihums go o(x) 5 x4 =x + ?.

\ghutagk : eakaeue go o(x)5 i0

@it x 5

i4

d

5

0

404=it x 5

4

=

5 0

9

eixaeue go o(x)

Bmklm rikcm as

,

0

9.

Mxiephm#9< : Oak` tbm rikcm go ritagkih mxprmssagk y 59xx

9xx4

4

ao x as rmih.

\ghutagk : y 59xx9xx4

4

(y 9)x4 + (y + 9) x + y 9 5 > ........(a)

lism- : ao y 9, tbmk mquitagk (a) as qui`rital ak x

ik` x as rmih

@ > (y + 9)4 0(y 9)4 > (y wbalb as pgssadhm is x as rmih.

Tikcm

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EIPB\

"eikasbfueirpbysals.ak" 2

\mho priltalm prgdhmes :

(99) A o l ; > ik` ix4 + 4dx + `gms kgt bivm iky rmih rggts tbmk prgvm tbit

(a) i 4d + (aa) i + 0d + 94l ; >

(94) Ao o(x) 5 (x i) (x d), tbmk sbgw tbit o(x) 0

)di( 4.

(9 x T.

(90) Oak` tbm rikcm go tbm mxprmssagk3x4x

39x) ; > ik` valmvmrsi.

Sm cmt sax `aoomrmkt pgsatagks go tbm cripb watb rmspmlt tg x ixas is sbgwk.

(a) Lgklhusagks :

(i) i ; >

(d) @ ; >

(l) Tggts irm rmih & `astaklt.(`) o(x) ; > ak x (,) (,)(m) o(x) 8 > ak x (,)

(aa) (i) i ; >

(d) @ 5 >

(l) Tggts irm rmih & mquih.

(`) o(x) ; > ak x T {}

(aaa) (i) i ; >

(d) @ 8 >

(l) Tggts irm aeicakiry.(`) o(x) ; > x T.

(av) (i) i 8 >

(d) @ ; >

(l) Tggts irm rmih & `astaklt.

(`) o(x) 8 > ak x (,) (,)(m) o(x) ; > ak x (,)

(v) (i) i 8 >

(d) @ 5 >

(l) Tggts irm rmih & mquih.

(`) o(x) 8 > ak x T {}

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EIPB\

"eikasbfueirpbysals.ak" 1

(va) (i) i 8 >

(d) @ 8 >

(l) Tggts irm aeicakiry.

(`) o(x) 8 > x T.

9>. \ghutagk go Yui`rital Akmquihatams:Pbm vihums go ' x ' sitasoyakc tbm akmquihaty ix4 + dx + l ; > (i >) irm:(a) Ao @ ; >, a .m. tbm mquitagk ix4 + dx + l 5 > bis twg `aoomrmkt rggts & sulb tbit 8

Pbmk i ; > x ( ) ( )i 8 > x ( )

(aa) Ao @ 5 >, a.m. rggts irm mquih, a.m. 5 .Pbmk i ; > x (,) ( )

i 8 > x

(aaa) Ao @ 8 >, a.m. tbm mquitagk ix4 + dx + l 5 > bis kg rmih rggt.

Pbmk i ; > x Ti 8 > x

(av) Akmquihatams go tbm ogre.........)x(L)x(D)x(I

.........)x(T)x(Y)x(^

> lik dm qualfhy sghvm` usakc tbm emtbg` go

aktmrvihs, wbmrm I, D, L........, , Y, T......... irm hakmir oukltagks go ' x '.

Mxiephm#9= : \ghvm9x

3x?x4

4

4

\ghutagk : x4 + ?x 3 4x4 + 4 x4 ?x + 1 > (x x T

Mxiephm # 9? :\ghvm|9x|

9xx4

; >.

\ghutagk :|9x|

9xx4

; > ........(a)

|x + 9| ; >, x T {9} (a) dmlge ms x4 + x + 9 ; > x 9 x4 + x + 9 ; >, x T (is ats i ; > ik` @ 8 >) \ghutagk go (a) as x T {9}

Mxiephm#93: \ghvm9xx

9x

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EIPB\

"eikasbfueirpbysals.ak" 9>

\mho priltalm prgdhmes :

(9?) \ghvm tbm oghhgwakc akmquihatams :

(a) |x4 + x | = 8 > (aa) x4 3x + 94 8 |x 0|

(93) \ghvm :1x

x44

4x

9

(92) \ghvm tbm akmquitagk : (x4

+ tg dm crmitmr tbik i spmlaoam` kuedmrx> irm

d 0il > & o (x>) ; > & ( d/4i) ; x

>.

(aa) Lgk`atagks ogr dgtb tbm rggts go o (x) 5 > tg dm seihhmr tbik i spmlaoam` kuedmr x> irm

d 0il > & o (x>) ; > & ( d/4i) 8 x

>.

(aaa) Lgk`atagks ogr i kuedmr x> tg ham dmtwmmk tbm rggts go o (x) 5 > as o (x

>) 8 >.

(av) (v)

(av) L gk`at agks tbit dgtb rggts go o (x ) 5 > tg dm l gko a km` dmtwmmk tbm kuedmrs x9

ik `

x4, (x

98 x

4) irm d 0il > & o (x

9) ; > & o(x

4) ; > & x

98 ( d/4i) 8 x

4.

(v) Lgk`atagks ogr mxilthy gkm rggt go o (x) 5 > tg ham ak tbm aktmrvih (x9, x

4) a.m.

x9

8 x 8 x4

as o (x9) . o ( x

4) 8 >.

Mxiephm#92: Hmt x4 ( e (eT) dm i qui`rital mquitagk, tbmk oak` tbm vihums go 'e' ogr wbalb

(i) dgtb tbm rggts irm crmitmr tbik 4.(d) dgtb rggts irm pgsatavm.

(l) gkm rggt as pgsatavm ik` gtbmr as kmcitavm.

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EIPB\

"eikasbfueirpbysals.ak" 99

( ) Gkm rggt as crmitmr tbik 4 ik` gtbmr seihhmr tbik 9

(m) Tggts irm mquih ak eickatu`m ik` gppgsatm ak sack.

(o) dgtb rggts ham ak tbm aktmrvih (9, 4)

\ghutagk : (i)

Lgk`atagk - : @ > (e e4 9>e + 1 > (e 9) (e 1)> e (, 9U V1,) ......(a)

Lgk`atagk - : o (4) ; > 0 (e e 8 9> ......(aa)

Lgk`atagk - : i4

d; 4 4

4

)

(d)

Lgk`atagk - @ > e (, 9U V1,)Lgk atagk - o(>) ; > e ; >

Lgk`atagk -i4

d ; >

4

e ; ) 8 > e 8 > I ks .

(`)

Lgk`atagk - o(9) 8 > 0 8 > e Lgk atagk - o(4) 8 > e ; 9>Aktmrsmltagk cavms e Iks.

(m) sue go r ggts 5 > e 5 ) 8 > e 8 >

e Iks.

(o)

Lgk`atagk - @ > e (, 9U V1,)Lgk`atagk - o(9) ; > 9 (e 0 ; >wbalb as trum e T

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EIPB\

"eikasbfueirpbysals.ak" 94

Lgk`atagk - o(4) ; > e 8 9>

Lgk`atagk - _ 9 8 i4

d8 4 9 8

4

i ; 4Lgk`atagk- : o(4) ; > (i 4)0 0i + i + < ; >

i = ; > i ; =

Lgk`atagk- : o(9); > 0i + 9 ; > i ; 0

9

Lgk`atagk- : @ > 0i4 0(i + i ?

Lgk`atagk-_ : 4 8 i4

d8 9 i (, 9) (0,)

Aktmrsmltagk cavms i(=, ?U. Ik s.

Lism- wbmk i 4 8 >i 8 4

Lgk`atagk - o(4) 8 > i 8 =

Lgk atagk - o(9) 8 >, i 8 0

9

Lgk`atagk - 4 8 i4

d8 9 i (, 9) (0,)

Lgk`atagk -_ @ > i ?

aktmrsmlta gk cavms i

0

9,

lgephmtm sghutagk as i

0

9, (=, ?U Iks.

\mho priltalm prgdhmes :

(49) Hmt 0x4 0( 4)x + 4 5 > ( T) dm i qui`rital mquitagk, tbmk oak` tbm vihum go '' ogr wbalb(i) Dgtb tbm rggts irm pgsatavm (d) Dgtb tbm rggts irm kmcitavm

(l) Dgtb tbm rggts irm gppgsatm ak sack. (`) Dgtb tbm rggts irm crmitmr tbik 9/4.

(m) Dgtb tbm rggts irm seihhmr tbik 9/4.

(o) Gkm rggt as seihh tbik 9/4 ik` tbm gtbmr rggt as crmitmr tbik 9/4.

(44) Oak` tbm vihums go tbm piriemtmr 'i' ogr wbalb tbm rggts go tbm qui`rital mquitagk

x4 + 4(i 9)x + i + = 5 > irm

(a) pgsatavm (aa) kmcitavm (aaa) gppgsatm ak sack.

(4px + (4=p4 + 9=p ??) 5 >

irm hmss tbik 4.

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EIPB\

"eikasbfueirpbysals.ak" 9 ( T) dm i qui`rital mquitagk, tbmk oak` tbm vihums go '' ogrwbalb

(a) Mxilth y gkm rggt ha ms ak

4

9,> . (aa) Dgtb rggts hams ak

4

9,> .

(aaa) It hmist gkm rggt hams ak

4

9,> .

(av) Gkm rggt as crmitmr tbik 9/4 ik` gtbmr rggt as seihhmr tbik >.

(4?) Oak` tbm vihums go i, ogr wbalb tbm qui`rital mxprmssagk ix4 + (i 4) x 4 as kmcitavm ogr

mxilthy twg aktmcrih vihums go x.

Ikswmrs : (49) (i) V

4

i

i

, 9 4

, tbmk tbm pghykgeaih o(x) as mxilthy`avasadhm dy (x ) gr(x ) as i oiltgr go o(x) ik` lgkvmrsmhy.

( aa) Mvmry mquita gk go ktb `mcrmm (k 9) bis mxilthy k rggts & ao tbm mquitagk bis egrm tbik k rggts,at as ik a`mktaty.

(aaa) Ao tbm lgmooalamkts go tbm mquitagk o(x) 5 > irm ihh rmih ik + aas ats rggt, tbmk aas ihsg irggt. a.m. aeicakiry rggts gllur ak lgkjucitm piars.

(av) Ik mquitagk go g`` `mcrmm wahh bivm g`` kuedmr go rmih rggts ik` ik mquitagk go mvmk `mcrmm

wahh bivm mvmk kuedmrs go rmih rggts.

(v) A o tbm lgmoo al amkts ak tbm mquitagk irm ih h rit agkih & + as gkm go a ts rggts, tbmk

as ihsg i rggt wbmrm, Y & as kgt squirm go i ritagkih kuedmr..(va) Ao tbmrm dm iky twg rmih kuedmrs 'i' & 'd' sulb tbit o(i) & o(d) irm go gppgsatm sacks, tbmk

o(x) 5 > eust bivm g`` kuedmr go rmih rggts (ihsg ithmist gkm rmih rggt) dmtwmmk ' i ' ik` ' d '.

(vaa) Mvmry mquitagk o(x) 5 > go `mcrmm g`` bis ithmist gkm rmih rggt go i sack gppgsatm tg tbit go ats

hist tmre. (Ao lgmooalamkt go bacbmst `mcrmm tmre as pgsatavm).

Mxiephm#4> : Ao 4x< + bis rggts,, tbmk oak` + +, + + ik`.

\ghutagk : ]sakc rmhitagk dmtwmmk rggts ik` lgmooalamkts, wm cmt

+ + 5 5 4< , + + 5

4= , 5

4? 5

8/12/2019 Quadratic Equation Theory_e

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