Question

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

A. 4 

B. 3 

C. 2 

D. 1

Answer 1

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)