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Algebra

Hot goIITian

Joined: 7 Aug 2007
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4 Apr 2008 21:36:56 IST
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complex:JEE question
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what is the value of p and q if 2+ i sqrt3 is a root of eqn x^3 + px + q = 0?
 


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arpan1's Avatar

Blazing goIITian

Joined: 15 Mar 2008
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4 Apr 2008 21:41:38 IST
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assuming that the co-efficients of the eqn are all real

then we have two roots are 2+sqrt (3)i  and 2- sqrt.(3)i and -4
(since sum of roots is zero)


p = -9 (product taken 2 at a time)


q= 28 ( negative of  product of 3 at a time)


rate me

Hot goIITian

Joined: 7 Aug 2007
Posts: 184
4 Apr 2008 21:43:50 IST
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sorry dude..answer is p=-4 and q=7
arpan1's Avatar

Blazing goIITian

Joined: 15 Mar 2008
Posts: 684
4 Apr 2008 21:45:56 IST
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the method is right

either u hav written the ques wrong or the ans is wrong !!!

Hot goIITian

Joined: 7 Aug 2007
Posts: 184
4 Apr 2008 21:50:17 IST
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may be..its from FIITJEE material..and sometimes there is printing mistake...
arpan1's Avatar

Blazing goIITian

Joined: 15 Mar 2008
Posts: 684
4 Apr 2008 21:51:33 IST
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tell me from which fiitjee packet
Ajitha's Avatar

Blazing goIITian

Joined: 10 Nov 2007
Posts: 473
5 Apr 2008 02:23:37 IST
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what arpan said was ryt.......i think the q is x2 +px+q and not.......x3 +px+q

if so...............

complex roots occur in conj pairs..........

terefore if 2+i[ 2] 3 is a root then 2-i[2 ] 3 is also a root..............

sum of them =4

product of them = ( 4+ 3) =7

terefore the eqn with these as roots is : x2-4x+7 = 0


hence p=-4 and q =7



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