Hi everyone and welcome to MathSux! In this post, we are going to answer the question, what is the discriminant? Before going any further, if you need a review on what the quadratic equation or imaginary numbers are, check out each related link! Also, don’t forget to check out the video and practice questions below. Happy calculating! 🙂

**What is the Discriminant?**

The **discriminant** is a formula we can use that tells us more about a quadratic equation including:

- The number of solutions a quadratic equation has.
- The “nature” of the roots of the solution (rational/irrational or real/imaginary).

**Discriminant Formula:**

The** discriminant** formula may look familiar! It is part of the quadratic formula and we have seen it before, using the very same coefficients a, b, and c from the quadratic equation.

**How does it Work?**

When we find the value of the discriminant of any quadratic equation, it will give us a value that tells us how many solutions (or roots) a quadratic equation has. Remember when we say “roots” what we really mean are the x-value(s) of the quadratic equation that hit the x-axis. This value will also tell us if the solutions to the quadratic equation are rational/irrational or real/imaginary. Take a look at how it all breaks down below:

Now that we are familiar with the rules, let’s take a look at an **Example**:

**Step 1: **First let’s write out our quadratic equation and identify the coefficients a, b, and c so they are ready to be plugged into our discriminant formula.

**Step 2: **Now let’s write out and fill in our formula using the coefficients and solve.

**Step 3: **Now let’s analyze our answer! Since, we got a discriminant value of 36, notice that it is a **positive** **perfect square**! If we look back at our discriminant table, this tells us that our quadratic equation is going to have **2 real and rational solutions**.

**Practice Questions:**

Find the discriminant, number of solutions and nature of the roots of the following quadratic equations:

**Solutions:**

Still got questions? No problem! Don’t hesitate to comment with any questions below or check out the video above. Thanks for stopping by and happy calculating! 🙂

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