If we define a quadratic for a,b,c ∈ R and a ≠ 0 , ax^2 + bx + c = 0 ; there is no real solution for Δ < 0 However if we change the defination to for a,b,c ∈ Q and a ≠ 0 , ax^2 + bx + c = 0 ss = ∅ , this time our equation includes imaginary numbers too therefor we can get a solution set
for x ∈ R, x^2 +16 = 0 --> ss = ∅
for x ∈ Q, x^2 +16 = 0 --> x^2 = √-16 = 4i ss = { -4i , 4i}