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?

Let roots be α, β. After squaring, roots are α², β². For unchanged equation, {α, β} = {α², β²}. Cases: (i) α = α², β = β² gives α, β ∈ {0, 1}, yielding pairs (0,0), (0,1), (1,1) — three equations: x², x(x−1), (x−1)². (ii) α = β², β = α² with α ≠ α²: α = α⁴ gives α³ = 1, α ≠ 1, so α is a primitive cube root of unity. This gives one equation x² + x + 1 = 0. Total = 3 + 1 = 4.