The discriminant is a special part of math, shown as $D = b^2 - 4ac$. It helps us learn about the solutions, or roots, of a quadratic equation written like this: $ax^2 + bx + c = 0$.

Here’s how the value of the discriminant tells us about the roots:

1. Two Different Real Roots:

   • If $D > 0$, the equation has two different real roots. This happens when the graph of the equation, called a parabola, crosses the x-axis at two places. For example, if $D = 9$, there are two real roots.

2. One Real Repeated Root:

   • If $D = 0$, there is just one real root, which we call a double root. This means the parabola touches the x-axis at one point. For instance, when $D = 0$, that’s what happens.

3. Two Complex Roots:

   • If $D < 0$, the equation has two complex roots, which are related to each other in a special way called conjugates. In this case, the parabola doesn’t touch the x-axis, which means there are two imaginary solutions, like when $D = -4$.

To sum it up, the discriminant is a helpful tool that tells us what kind of roots a quadratic equation has:

• Two different real roots,
• One repeated real root, or
• Two complex roots.

It all depends on the value of $D$.