IIT JEE , AIEEE Forum - Mathematics , Algebra

akhil_o

Find the coefficient of
x⁵⁹ in
(x-1)(x²-2)(x³-3)..(x¹¹-11)

hash_include

-7 + 6*1 + 2*5 + 3*4
??

akhil_o

dunno the answer...
but yeah 21 was an option...marked it as 21 too!! ;)

how did u do it?

hash_include

by logic only..
see the degree of the polynomial is 1+2+3... 11 = 66
so, to find a term with x^59, you have to remove an x^7 somehow..
that can be done by multiplying all the x terms except x^7 but instead, you have to multiply by -7 as you're not multiplying x^7.
similarly, a x^4 and x^3 should be removed and replaced by (-3)*(-4)
and similarly for 5,2 and 1,6

i know ive not been clear in my words here, so if youve any problem understanding what ive written, pls ask :)

akhil_o

no no i understood, i did it the same way
was wondering if there was a different shorter apprach and a general approach to avoid too many calculations

LAMPARD

But suppose,you multiply x¹¹*x¹⁰*...x⁵...So,it becomes x⁵⁶
So,now,you need an x³ term...so, you will also have (-1)(-4)(-2) right...But,you havent considered it in ur answer...

(**338**)

plz explain.

hash_include

s.h.i.t s.h.i.t s.h.i.t s.h.i.t!!! lampard youre right!!
somebody KILL ME!! :( :(
i forgot to take combinations of 3 or more x power terms!
so sorry akhil, but youve to consider -1*-2* -4 also
so answer is 13!

akhil_o

damn!!
u just made me wrong ;)

thnx a lot ppl
:)
ne other methods?

computer001

this is basically probability:
integers which can sum up to 7 are: (7),(6,1),(5,2),(4,3),(2,4,1)
hence v have (-1)^1*7 + (-1)^2*6 + (-1)^2*12 +(-1)^2(10) + (-1)^3*(8)
=-7+6+10+12-8=13

EDITed

computer001

oops din c the last few posts

elastiboysai

See this
a similiar question

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