The discriminant of ax² + bx + c is:

The discriminant of a quadratic expression of the form $ax^2 + bx + c$ is a specific value that helps determine the nature of the roots (real, equal, or complex). ### Step-by-Step Explanation: 1. **Identify the Standard Form**: A quadratic equation is typically written as $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants. 2. **Recall the Quadratic Formula**: The solutions for $x$ are given by: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. **Isolate the Discriminant**: The expression found under the square root symbol in the quadratic formula is called the **discriminant**. It is denoted by the symbol $\Delta$ (Delta) or $D$. 4. **Final Formula**: Therefore, the discriminant is: $$\Delta = b^2 - 4ac$$