The number of quadratic equations having real roots and which do not change by squaring their roots is

The roots of the equation are real (given)

Let α and β be the two roots according to the given condition


α = α2


β = β2


Sum of the roots = α + β = α2 + β2


Product of the roots = α β = α2 β2


There are only two number who does not change on squaring them that is 0 and 1


So the number of equations could be 2 by being the roots as


(0,1) and (1,0)

15