To find the Discriminant of a quadratic equation, we usually write it as ( ax^2 + bx + c = 0 ).

The formula to use is:
[ D = b^2 - 4ac ]

Don't worry! It’s pretty simple once you get the hang of it. Here’s how you do it step by step:

1. Find a, b, and c: Look at your equation and figure out the values for ( a ), ( b ), and ( c ).

2. Use the formula: Take the value of ( b ) and square it (that means multiplying it by itself). So you get ( b^2 ). Then, from this, subtract ( 4 \times a \times c ).

3. Do the math: Now, just work out the math, and you’ll find your Discriminant ( D ).

Now, what can the Discriminant tell us about the roots (the solutions) of the equation? Think of it as a secret guide! Here’s what to keep in mind:

• If ( D > 0 ): There are two different real roots.
• If ( D = 0 ): There is just one real root (or it’s a root that repeats).
• If ( D < 0 ): This means there are no real roots, but there are two complex roots instead.

So, the Discriminant is really useful for figuring out what kind of roots your quadratic equation has!