In the quadratic equation, b^2 - 4ac < 0.

If the determinant of the quadratic (ax² + bc + c) as worked out by b² - 4ac is a perfect square or not. If the determinant is not a perfect square then the roots are irrational.

None, if the coefficients of the quadratic are in their lowest form.

The discriminant must be a positive number which is not a perfect square.

By using the quadratic formula the given quadratic expression will factor into irrational numbers and so therefore a straight forward answer is quite difficult.