If the highest degree coefficient is equal to 1, then what is the total number of quadratic equations which are unchanged on squaring their roots ?

Explanation

Let the roots be a and b. For the equation to remain unchanged, we must have a^2 = a and b^2 = b. The possible root sets yielding real coefficients are {0,0}, {1,1}, {0,1}, and {\omega, \omega^2}. This results in exactly 4 such equations.

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