If the discriminant equals zero, how many real roots does the equation have?

The discriminant is an important component in determining the nature and number of roots of a quadratic equation, typically presented in the form ( ax^2 + bx + c = 0 ). The discriminant is calculated using the formula ( D = b^2 - 4ac ).

When the discriminant is equal to zero, this indicates that there is exactly one unique solution for the quadratic equation. In such a case, the equation has one real root, which is referred to as a repeated root or a double root. This means that the parabola represented by the quadratic equation touches the x-axis at a single point rather than crossing it.

The concept of rationality or irrationality of roots pertains to whether the roots can be expressed as simple fractions or not. However, when the discriminant is zero, it confirms there is one real root, regardless of its classification as rational or irrational. The classification into rational or irrational roots typically comes into play when the discriminant is positive and not a perfect square, or negative, but with zero, the key takeaway is that a single real root exists.

Therefore, the correct understanding is that when the discriminant is zero, the quadratic equation has one real root, which emphasizes its uniqueness rather than involving