My friend asked me this puzzle:
The number of quadratic equations which are unchanged by squaring their roots is
My answer is: 3
$x^2-(\alpha+\beta)x +\alpha\beta = 0$
where $\alpha$ and $\beta$ be the roots.
case 1: $\alpha$ = 0 $\beta$ = 0
case 2: $\alpha$ = 1 $\beta$ =1
case 3:$\alpha$ = 0 $\beta$ = 1
But my friend says answer is 4. How come?