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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?

2 Answers 2