Let the two roots be α,β.
f(x)=(x−α)(x−β)=0
Roots are squared α2,β2
Roots remain same as even after squaring,
α=α2, β=β2⇒α=0,1⇒β=0,1
(roots are real)
So, α=0,β=0⇒x2=0
α=1,β=1⇒(x−1)2=0α=0,β=1⇒x2−x=0α=1,β=0⇒x2−x=0
Hence, there are 3 quadratic equations possible.