1. The problem asks about the roots of a quadratic equation. 2. A quadratic equation is generally written as $ax^2 + bx + c = 0$ where $a \neq 0$. 3. The roots of the quadratic equation are the values of $x$ that satisfy this equation. 4. The roots correspond to the solutions of the equation and can be found using the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 5. Here, $b^2 - 4ac$ is called the discriminant and determines the nature of the roots: - If the discriminant is positive, there are two distinct real roots. - If it is zero, there is exactly one real root (a repeated root). - If it is negative, the roots are complex conjugates. 6. The roots correspond to the $x$-intercepts of the parabola represented by the quadratic function $y = ax^2 + bx + c$. 7. Thus, the roots of a quadratic correspond to the points where the graph of the quadratic crosses or touches the $x$-axis.