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Pbgyalajgbr Dfassms
PLD/Quagratbd Mquatbijs & Bjmquatbijs 1 H^W-Tifutbijs/Lathmlatbds
Annarwaf Dirpiratm Hmbnhts, 4rg @fiir, Ufit Ji. A - >, Jmtakb Tuohash Ufadm,
Ubtal Uura, Gmfhb - 115547 Uhijm; 511-7=??1125-24.
Tifutbijs ti Hilm ^irc Wmst/Lathmlatbds
?.
4
4? ? 4 44 ? 4
44
?
a a a
a
4 ?
?
?> 18
18 ?>
? ?
aa a
a
a
Asa6 5, 18a?> 6 5 ajg ?a?: 5
?
18 ?>5
?
a
a
Ti, ajswmr bs iptbij (G).
4. a o a ajg ao
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Pbgyalajgbr Dfassms
PLD/Quagratbd Mquatbijs & Bjmquatbijs ? H^W-Tifutbijs/Lathmlatbds
4.?
? 5ax dx o ajg ? ? 5ax ox d havm a dillij riit b`
?
? ? ? ?a o a d . d d o o a d a o
ir ?? ?? ? ? ?ao ad . d o ad ao ir ? ??7a d o d o a d o
ir ?7a d o a (Tbjdm do)
ir 7 7d o a ir 7 7 5a o d
8. Fmtom a riit i` ? 5x x l . Whmj ?bs a riit i` ? 4 ? 5x x l
? 5l ajg ?7 0 ? 5l ir ?? 4 5l . . . .(bb)
ir?
? ? ? 5l . . . .(b)
Tuotradtbjn (bb) `ril (b), wm nmt ;
5l ir 7 5a a a a
7
4a ajg ?7 7 5a a
Quagratbd Mquatbijs & Bjmquatbijs H^W - 4
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Pbgyalajgbr Dfassms
PLD/Quagratbd Mquatbijs & Bjmquatbijs 4 H^W-Tifutbijs/Lathmlatbds
7
4a ajg 1 5a a
7
4a ajg 5 1a ,
5 1a ,
8. Fmt riits om p qb ajg p qb (_iits wbff mxbst bj dijkunatm-pabr)
? ?p q
Jiw, ? ? d
p qb p qb p qa
Tbjdm 1d
a d,a
ir ? ? 1p q ir ? ? 1p q
15. Gmtmrlbjajt i` ?1 7` x G o ad
Gmtmrlbjajt i` ?? 7n x G o ad
?1 ? ? 5G G o Atfmast ijm i` G1ajg G? 5
5` x . n x has at fmast twi rmaf riits.
0. Fmt ` x x a x o x o x d x d x a
` a a o a d , ` o o d o a , ` d d a d o
Tbjdm`(x) bs syllmtrbd wbth rmspmdt ti a, o ajg d. Fmt us assulm that a 6 o 6 d. Whmj 5 5` a , ` o ajg 5` d .
5` a . ` o ajg 5` d . ` o
`(x) has ijm riit bj x a, o ajg ithmr riit bj x o, d `(x) has rmaf riits.
1. 1a o
x a x o
nbvms a x o o x a x a x o
ir ? ? 4 5x a o x ao
Tbjdm riits arm mquaf bj lanjbtugm out ippisbtm bj sbnj, sul i` riits < 5 < ?(a + o) a + o < 5
?. ?
Tbjdm , arm riits i`? 5x px r , p ajg r
? p r
Tbjdmbs a riit i` ? ?5 5x px q , p q ir ? p q
q r
4. Fmt , om riits i`?
5x px q . Whmj c , c daj om tacmj as riits i` ? 5x fx l
p ajg q ajg c ajg ?c l
@ril aoivm mquatbijs wm nmt ;
? ??
?
lc
q p p
? ?p l f q
Quagratbd Mquatbijs & Bjmquatbijs H^W - 7
Quagratbd Mquatbijs & Bjmquatbijs H^W - =
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8/13/2019 Jee 2014 Booklet1 Hwt Solutions Quadratic Equations & Inequations
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Pbgyalajgbr Dfassms
PLD/Quagratbd Mquatbijs & Bjmquatbijs = H^W-Tifutbijs/Lathmlatbds
Jiw, dijsbgmr ? 5x
Whm mquatbij omdilms 4 ? 1x . x ir ? 4xx
^m nmt ajithmr sifutbij i` thm mquatbij.
Tblbfarfy, thmrm mxbsts a sifutbij whmj 5 ?x ajg thmrm mxbsts a sifutbij whmjx: ?.
Ti, thmrm arm 7 sifutbijs.
7. Tmm thatx< 1 bs a sifutbij i` thm nbvmj quagratbd mquatbij. Hmjdm, (G) bs thm dirrmdt iptbij.
=.7
7 1 5x x nbvms 7 7 1x x
@ril thm `bnurm bt bs dfmar that thm nbvmj mquatbij has ? pisbtbvm rmaf riits.
0.7
7 1 5x x nbvms 7 7 1x x
@ril thm nraph bt bs dfmar that thm nbvmj mquatbij has ijm jmnatbvm rmaf riit.
>. @ril thm aoivm nraph wm smm that thmrm arm ? rmaf riits `ir thm mquatbij7
7 1 5x x . Whm mquatbij has 7 riits. Hmjdm rmlabjbjn ?
riits arm dilpfmx riits.
8. ? ?
? ? 1 5a o x a o d x . Fmt us dhmdc G.
? ?
7 ? 7 7 ? ? ? ? 10G a o d a o o d a d o d a d
As 5a d o, o d ajg 5a d G 6 5 Whm riits i` thm nbvmj mquatbij arm blanbjary.
=. o ajg d
Jiw, o d ajg od
Ti, thm mquatbij whism riits arm o ajg d bs ? 5x x
8. o ajg 1
Jiw, `ir thm rmqubrmg mquatbij sul i` riits . ?
> 7 4 ? 4 ? 4x
1 1? 4 ? 4 ? 4 7? 4
xx
15. Fmt thm riits om ?,
Whmj?
1 5 ajg ? 4 c ir ? 1 5
4
41 = 1 = = 4 = 1=1 =
? 8 8
? = c
ir ? =c Ajswmr bs iptbij (D).
7. As thm mquatbij ? ? 4 5ax ox d has ji rmaf riits, G 6 5.
? ?7 7 4 7 4 5o a d o ad
Dijsbgmr ? ? 4` x ax ox d
5 4` d ajg 4
? 7 7 4 7 57
d` a o d a o
Jiw as G 6 5 `ir `(x), bt has salm sbnj x _ . As`(?) : 5, thmj`(5) : 5 4 5d ir d6 5.
0. Whm mquatbij?
5x ax o has mquaf riits whbdh arm?
ax . Addirgbjn ti thm qumstbij
?
ax bs a riit i` mquatbij
??
5 57 ?
a adx dx g g ir ? ? 7 5a ad g . . . .(b)
^m afsi havm G < 5 `ir thm mquatbij?
5x ax o
? 7 5a o ir ? 7a o . . . .(bb)
]sbjn (bb) bj (b) wm nmt ;
7 ? 5o g ad ir ?ad o g
Quagratbd Mquatbijs & Bjmquatbijs H^W - 2
Quagratbd Mquatbijs & Bjmquatbijs H^W - 15
