If the discriminant equals 0, the quadratic has:

The nature of the roots of a quadratic equation $ax^2 + bx + c = 0$ is determined by the discriminant, denoted by $D$ or $\Delta$, where: $$D = b^2 - 4ac$$ The roots of the quadratic equation are calculated using the quadratic formula: $$x = \frac{-b \pm \sqrt{D}}{2a}$$ Depending on the value of $D$, three cases arise: 1. **If $D > 0$**: The square root $\sqrt{D}$ is a positive real number. This results in two distinct real roots: $x_1 = \frac{-b + \sqrt{D}}{2a}$ and $x_2 = \frac{-b - \sqrt{D}}{2a}$. 2. **If $D = 0$**: The square root $\sqrt{0}$ is $0$. The formula becomes: $$x = \frac{-b \pm 0}{2a} \implies x = \frac{-b}{2a}$$ Both roots are exactly the same value, resulting in **two equal real roots** (also called a repeated root). 3. **If $D < 0$**: The square root of a negative number is not a real number, so there are **no real roots**. Since the question specifies $D = 0$, the quadratic has two equal real roots.