a problem

let the roots be x,y

thus on sqarring , roots are x²,y²

there are two possibilities ,

x=x² and y=y²

x=0,1 y=0,1 (3 solns.)

other possibility ,

x=y² y=x²

or x = x⁴ and y=y⁴

x(x³-1)=0 and y(y³-1)=0

x=0,1,ω,ω² y=0,1,ω,ω²

thus all solns. are ,

(1,1)
(1,0)
(0,0)
(ω,ω²)

Ans:4

aditya you want to say ω=ω².
On squaring ω we dont get the same answer.

(ω,ω²)

on squarring ,

(ω²,ω)

same roots , thus same equation.

THanks!

A couple of points:
Firstly for a Quadratic to remain unchanged its coefficients must be unchanged...

Σx²=Σx and Î x=Î x²

So that gives (x+y)=2,-1 with xy=±1

So altogether 4 such equations (It is unnecessary to get the solutions)

Secondly I doubt whether the list of solutions that Aditya has given is exhaustive. I think there are a couple of more solutions (provided I haven't screwed up my calculations again)

plz disclose the "couple of more solutions" . (because i am not getting any)