IIT JEE , AIEEE Forum - Mathematics , Algebra

kishan12

in a equation of power n......then n is the no of maximun no. of roots or it has to have n roots only?
Find no of roots of Z^4+Zbar=0......here see i put Z=a+ib ..........then again we get a equation...but then how to decide no of roots????
i am having this problem of finding max no of roots of an equation since long:(
Ans to that question is 5

elastiboysai

Are u sure d ans to your qn is 5?

I think it's 6.

kishan12

no the ans is 5..
but plzz tell how u got 6?...........i was gettin 4.........lol

elastiboysai

See the fact that an nth degree eqn can have only n roots is true for a polynomial equation with rational coefficients.

when u bring in complex numbers and their conjugates, theres a discrepancy.

for ur eqn

z^4+z'=0 (z'-- conjugate.)

z^4=-z'

take modulus

|z|^4=|z|

so |z|=0 or |z|=1 (the other 2 solns are meaningless)

|z|=0--->z=0 1 soln

|z|=1--->|z|^2=0--->zz'=0

z'=1/z

substitute

z^4+1/z=0

z^5=-1

this eqn obv has 5 roots

total 6 roots

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