A quadratic question

There are 4 possibilities where squaring the roots does not change the quadratic

$(0,0$ )

$(0,1$ )

$(1,1$ )

$(\omega, \omega^{2}$ )

Where $\omega , \omega^{2}$ are imaginary cube roots of unity.

Extras

Imaginary cube roots of unity are reciprocal , square , conjugate of each other.

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