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“ "f§core, , High“, , , , , , lth Q.E. (ALG) Sheet-1, Type —1 y $, 1. If the roots of Q. equestion x? — 4x —logsa = 0 are 4. For the equ 3x” + px + 3 = 0, p> 0 if one root of, , Real then find minimum value of ‘a’?, , , , 2.... Tf the roots of Q..equestion 2x? —4x-logiop =O... ., are Real then p-maximum is, (a) 100 (b) 10 (c)0(d) N.O.T., , 3; If one root of the Q. equestion ix? — 2(i + I)x +(2-i) = 0 is, , (2 —i) then the other root of equestion is, (ai ()2+I (A @NOT., , 4. S.T. the roots of Q.equ a(b—c)x” + b(c—a)x +, g c(a—b) = 0 are rational where a,b,ceQ, , 5. The roots of Q. equ (b+ c—2a)x* + (c+.a—2b)e, + (a+b —2c)=0 (where a,b,c €Q) are :, (a) Real (b) Irrational (c) rational (d) Imaginary, , , , 1 :, 6. If, is a root of the equx* + px+q=0, 5+iN3 a, (where p,q €R) then find the value of p&q., , * Note:- If a,b,c are odd integer then roots of q. equ ax +, “bx +e¢=0 can not be rational., , ie —2, 1. If pr = 2(q + s) then S.T. at least one of equ x” —, : px +q=0 and x*—rx+s=0 has real roots where, P.qr,seR., , 2. PLT. the roots of equ bx? + (b—0)x + (b—c—a)=, 0 are real & distinct. If the equ ax” + 2bx +b =0, has imaginary root where a,b,ceR., , Type-3, dy If the roots of equ px + qx +r=0 are in the ratio, , 3:2 then (a) 6p* = 25gr (b) 67 = 25pq, (c) 6g? = 25pr (@) N.O.T., , 2. If one root of the q. equ (/—m)x? + x + 1=0 be, double the other and ‘? is real then find, maximum value of ‘m’., , 3. If one root of the Q. equ ax” + bx +c =0 is equal, , _, to the n™ power of the other then P.T. (ac")"+, , +, (a"c)*! +b=0, , equ is square of the other then ‘p’ is equal to, , @A ML OI@NOT, oi, , “If the roots of x* — ax + b = 0 are two consecutive, odd integers then a” — 4 is equal to, (2)4 ()-4 (0) 14 @) NOT., , If the roots of x — bx + c= 0 are two consecutive, integers then b” — 4c is equal to, (a) 4 &)-4 ©14 @NOT., , If sec@ & cosec @& are roots of the equx’—px+ q=0, then (a) p= 4(q + 2) (b) p=q+2, ©g@=pe+2) @NO.T., , If sina &cosec@ are roots of equ px’ + gx +r=0, then (a)p*—q?+2pr=0 (b)p? + q+ 2pr=0, (©)p’-¢-2pr=0 (d)N.O.T., , Type-4, , 1, , If the Q. equx*—x+3a=0 and 2°-x+a=0, have a common root then find the value of ‘a’?, , The value of ‘k’ for which the equ x - kx —21=, , 0 & x?—3k¢+ 35 =0 will have a common root is, @+4 &+1 © +3 @0 @NOT., , If? +3x+5=0& a? +bxt+c=0 havea, common root and a,b,cEN then minimum value, of a+b +cis equal to, , @3 )6@9 @NOT., , Ife taxt+1=0&x'+axr2+1=Ohavea, common root then, , (a)ac(-c0,-2) (b) ae{-2}, (c)ac(2,-0) (d)N.O.T., , Let (x) = 2x? + 5x+ 1, if we write f(x) as f(x) =, [a+ 1) @—2) + b@—2) @= 1) +e(x- 1) +, 1)] for real number a, b & c then, , (a) there are infinite nos. of choices for a, b&e, (b) only one choice for ‘a’ but infinite nos. of, choices for b & c, , (c) exactly one choice foreach a, b &c., (4) more then one but finite no. of coices for a,b &c., , If the Q. equ. 2x” + 5x + 1, can be written as, , an

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[ae +1) (@—2) + B(x-2) (x- 1) +ele- 1), , (x + 1)] =0 for real number a, b & c then, , _ (a) there are infinite nos. of choices for a, b&c, (b) only one choice for ‘a’ but infinite nos. of, choices for b &c, , (c) exactly one choice for each a, b &c., , (d) more then one but finite no. of coices for a,b _, &e., , ras B are the roots of the Q. equ ax? + bet e= a, ” “observe the lists givén below’ - ., , List I List II, 1, , 1, (A) @=B (1) (ac?)3 + (a?c)3 +b=0, (B) @=28 (1) 28? = 9ae, (C) a@=3B (3) B= 6ac, (D) a =f? (4) ) 36? = 16ae, (5)) B= 4acl, , (6) ) (ac? 3 + (a 3 =b, The correct match of List I from List II is, , A B Cc D, (a5 2 4 6, (b)5 2 1 4, (c)5 2 4 1, , (d) N.O.T.

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g Fscoretigh e, , Medical | WEE T XID XN UT-JEE 1 Xt Xt, , , , find the equation whose roots be 5 & (— 30)? :, , find the equation whose AM of roots is 8 and, . there G.M. is 52. . ss, , Find the equation whose sum of roots be 5 and, product of roots be (-3/2)?, , Ifar & Bare the roots of 7 + 5x+4=0 then, , , , equation whose roots are = 2 af $ a is, (a) 9? +3x+2=0 - (b)9x?+3x-2=0, (6) 9x7 -3x+2=0 (d) N.O.T., , Ifa & Bare the roots of equation x —x+1=0, , thena?+ 8?" is equal to, , (a)2 ()-1()1 @NOT., Ifa & Pare the roots of equation x —2x+4=0, , then the value ofa" + 8” will be, (a) 2°*! cos(n 70/3) (6) i2°*! sin(n 7/3), (c) 2" cos(n 2/3) (d) N.O.T., , Ifa= cos i sin then the Q. equation, , paces Toots ate at@tad&Badtat, ais (ax? +x42=0 (b)x-xt2= 0., (ce)? +x-2=0 NOT. ~, , Leta & be the roots of equation px + qx + r=,, , O.If p,q and r are in AP. ana a 4 then, , value of |a@ — Aris 8 ol, ot @NO.T., , Let p & q be real no. such that p+ 0, p? ¥*qandp*, “#+4, Ifa & Pare non zero complex no., , satisfying a + B= p &a°+ f° = q then the Q., equation having a / Band B/a as is Toots is, (2) @*+q) 7 (p'-2q)x + © +a), , 0) @- 9) 2 +p'-2g)x + @+y= 0, , (©) @+q) x? (p'¥2q)x + (p +g) =0, , 10., , 11., , 12,, , 13., , 14,, , High |, , , , , , , , XI 1 XL., ’ Sheet—2, , LIT=JEE, , (@)N.OT., , Ifa & Pare the roots of the equation ax + bx +¢, , - - = 6(-a; b,#0) the the equation whose roois are ~-- , , , , , 1s is (a) acx? - bx +1=0, aatb a+b, , (b) aexr*+bx+1=0 (0) acx*-bx-1=0, (@)N.OT., , If @, Bare the roots of the equation A (x7 — x) tx, +5=0& IFA, & A, are two values of A obtained, , @ Be Aen # FFs equal, , Bas &, (a) 4192 (6) 4144 () 4048. () N.O.T., , from, , Ifa & Bare the roots of equa’ + bx +c=0&, 1-8, B, , , , © and-—> then r, , a”, may be equal to (a) a + 2b, (c) abe, , px +qxt+r=0 has oot =, , Qb)atbt+e, (d) N.O.T., , Leta & Bare the roots of equa? + bx+c=0&, A=B? —4ac. Ifa + Ba? +B? & 03+ B are in, GP.then(a)A #0 (6) bA=0, , ()cA=0 (d) be#0, , ’ eis oF Q :, ThAPQR, ZR: if tan’ and tan ~-are the, roots of ax’ + bx +c=0 (ax 0) then, , @b=ate (b)c=a+b, ()b=c ()a=bt+e, , Type-6 (symmetric function of a & B), , 1,, , Ifa & Bare the roots of x? — ax + 5? =0 thena?+, A is equal to (a) a? +25? (b) a? - 20?, (a2 (d)N.O.T., , Ifa & Pare the roots of 7 ~ 2744 = 0 then the, value of ° + f° is (a) 32 (b) 128 (c) 56 (d)not., , Ifa & Bare the roots of 2 +3x—4=0 then the, , Ts 3, value of — + — j, =, a Be®, , i, oF.

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4 6., (= @NOT., 3, 4. Ifa & Bare the roots of 7 + 2bx +c = 0 then the, 2 2, os (@+B) ., bc is equal to EP (b) 4 7., 2, @ GA ()N.OT., 2 oe we ee RS, 5. Ifa & Pare the roots of x + px + q=0 then find, a B . 8., value of — + — +a‘+f'9, Boa”, 6. Ifa + B=—2 & a+ B =— 56 then Q.equ whose 9., _ Toots area & Bis (a) x7? +2x-8=0 ,, Q)P+2%x+8=0 ()2-2-8=0 MNOT., 7. far & Bare the roots of x +ax+ 5=0 then, 2 10., m 2, + = is equal to (a) < (b) es, ose” @NO.T., a, 11., Type~7 (symmetric function of@ , 3 & 7), 1s Find the cubic equ whose roots are 2,(-3) & 5? Lv, , 2;, , , , If @,,@,,@;,@, are the roots of the equx’ +(2—, , » ¥3)x? + (2 +43) =0 then the value of (Ia; ), , (1a )(1-a, )(1-a%,) is (@) 1 (6) 4 (©) 5 @not..Ifa ,B& y are the roots of the equ t4x+2=, 0 thena?+ f*+ is equal to, , @2 @)6 ©@-6 @NO.T., , Ifa , Bay are the roots of the equ x° — 6x2 +, , 11x +6=0 then dias + YBa is equal to, , (a) 168 (6) 96 ()786 (4) NOT., , Ifa, 8 & 7 are the roots of the equx?—2x + 1+, , 1, = 0 then value of) is, a+B-y, , @-3 ®-1 (0 @NorT,, , , , , , , , Page 4 ee, , , , Ifa ,B& y are the roots of the equx’— 2x7+3,), , i, , _4=0 then value of? 87+ By? + y’ar*is, , @-3 @-5 ©-7 @NOT., , Ifa, B& y are the roots of the equ 2 — 3x7+, , 6x + 1=0 then value ofa? + 8’ + y’ is equal to, , IS 2 4 @Not, (0-7... OF Os.. ONOF., , Ifa, B& y are the roots of the equx? + 2x’— 3x, , —1=0 then value ofa? + 8? + vis equal to, (a) 12 (13 (14 (NOT., , Ifa, 8 & y are the roots of the equ x°— 3x°+x, +5=0 then y=) a? + ay is satisfies the equ, (@y+y+2=0 ()y-y-y-2=0, Oy ty¥-y-3=0 @NO.T., , Ifx1, X2, x3 & xq are roots of the equ x4 -2xsin2Z, +2cos2 B—xcos B-sin B= 0 then tan” x, + tan™, ‘yy + tan, + tan x, is equal to, , (@) B wt-B ©-8 @NOT., , . Ifthe sum of two roots of x° + px*— gx +r =Oig, , zero, then pq is (a)~r(b) r (c) 2d (d)N.O.T., , The condition that x7— py? + gx —r=0 may have, two of its roots equal in magnitude but opposite, , in sign i = =p =q%, coe Pq (b) r=p’g (c) r=qp (d)

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-- Find.the cubic-¢, , S, , __Institute, , Find the Q. equ whose roo, , h ts are 3 times the roots, of 3ax’ + 3bx+c=0, , the roots of x° + 2x? -4x+1=0, , Find the equation whose, , Toots is negative to the, roots of xX. —8x +7=0, , Find the equation whose roots is Reciprocal to, the roots of x” — 8x +7=0, , Find the equation whose roots is twice to the, , roots of xX — 8x +7=0, , If sin = ain & sin are the roots of equ?, + bx” + cx+d=0 then find the equ whose roots, , 2x An 6n, are Sone cosee scosec —?, , If a, B,y are roots of x + 4x+1=0 then the, 2 2 2, , 2 A is, , Bty y+a’ at+p, (b) xP -4x+1=0, @NOT., , , , , , equ whose roots are, , , , (@)x+4x-1=0, (ec)? -4x-1=0, , If @& @’ are the two imaginary cube roots of:, , unity then the equ whose roots are aw!” & a @?*?, , is (a)xX +axt+a=0 (b) 7 +ax-a?=0, (0)? -ax+a"=0 @NO.T., , Type-9, 1., , , , Find the value of ‘a’ for which both the roots of, x +x+a=0 exceed ‘a’, , Find the value of ‘m’, equ? —mxt+1=, greater then 1., , for which one root of the, 0 is less then 1 and other is, , If roots of x*— (a— 3) x+a=0 are such that at, least one of root is greater than 2 then, , (a)a €[7, 9] (b) a €[7,00], , (c)a €[9,c0] ()N.O.T., , Find the value of ‘a’ for which ¥-(a-3)xta, = 0 has at least one positive root., , quation whose roots are Atimes. ., , 3, , QE. (ALG), , coreHigh |, , Sheet-3, , vi, , , , , , , , 5. If both the roots of the Q. equx?*— 2k +2 +k—, 5=0 are less than 5, then ‘k’ lies in the interval, -@I45] 2) OBO)..., (ce) C00,4) (d) N.O.T., Type-10, i All the values of m for which both roots of the, equ x° —2mx + m? — 1 = 0 are greater than (— 2), but less then (4) lies in the interval, (a) m>3 (b)-1<m<3, ()1l<m<4 (A) N.O.T., 2. If & (#0) is a root of equ ax’ +bx+c=0 &, 8 (#0) isa root of equ—ax* + bx +c=0 then, s.t. there is a root y of equ oF +bx+c=0, which is lie blwar & f., 35 Ifa, b, c be real, if ax* + bx -+e=0 has two real, rootsa@ & 8, wherea < -1& 8 >1, then1 toe, a, —| is equal to, a, (<0 (b)>0 () <0 © (NOT, Type—11, 2, Fs 2., 1. Ifx is real , then = re ** takes values in the, Interval, 1, @ [33] ©) ©3,3) ©G,3)@Nor,, 2., , Ifx is real, then values of — 7+, 2x? 43x46, , : 11 -1 1) terval (a)/ — 1 ae, sea o(34) o(34), , , , lies in the