What type of roots can be derived when the discriminant is positive?

When the discriminant of a quadratic equation (in the form (ax^2 + bx + c = 0)) is positive, it indicates that the equation has two distinct real roots. The discriminant is calculated using the formula (D = b^2 - 4ac).

When (D > 0), this means that the value of (b^2) is greater than (4ac), leading to a situation where the square root of the discriminant ((\sqrt{D})) is a real number. Consequently, because you are adding and subtracting a real number from (-b) in the quadratic formula (x = \frac{-b \pm \sqrt{D}}{2a}), the result will yield two distinct real values for (x).

Thus, the conclusion here is that a positive discriminant confirms the presence of two real roots. The roots can be either both rational or both irrational depending on the specific values of (a), (b), and (c), but what is significant in this context is the existence of real roots, regardless of their rationality or irrationality.