Quadratic Equations — MATHS STD 11 Science — Question

Let a and b be the real roots of the quadratic equation.
we need to find the number of quadratic equation such that they ramain unchanged even if roots are squared.
a² = a and b² = b
⇒ a(a - 1) = 0 and b(b - 1) = 0
⇒ a = 0 or a = 1 and b = 0 or b = 1
so we have four pairs of roots (0, 0), (0, 1), (1, 0), (1, 1)
For (0, 0)
(x - 0) (x - 0) = x²
for (0, 1)
(x - 0) (x - 1) = x (x - 1) = x² - 1
For (1, 0)
(x - 1) (x - 0) = (x - 1) x = x² - 1
For (1, 1)
(x - 1) (x - 1) = (x - 1)² = x² - 2x + 1
So there are 3 quadratic equations with real roots, which do not change by squaring their roots.