The solution of quadratic formula is represented as
x = -b ± squareroot (b^2 – 4ac) / 2a
Where b^2 – 4ac is known as the radicand.
Lets take an equation; x^2 + 6x + 5 = 0
Where a = 1, b = 6, c = 5
The solution will be x = -6 ± squareroot(6^2 – 4(1)(5)) / 2(1)
Where radicand = 6^2 – 4(1)(5) = 36 – 20 = 16
Hence radicand is the perfect square of 4. i.e. 4^2 = 16
Now solving the equation further;
x = (-6 ± 4 ) / 2
x = -1 , x= -5
Thus for a radicand to be a perfect square, the solution of a quadratic equation will composed of two different rational solutions.