I decided to do this because you can skip some steps if you find out the discriminant early ex. if discriminant is negative.

In a quadratic equation, we can determine the nature of x with the help of the discriminant. The discriminant refers to the radical in the quadratic formula,

The nature of x can be determined with the following guidelines.

• If the radical is positive, there are 2 solutions (real & unequal).
• If the radical is 0, there is 1 solution (real & equal).
• If the radical is negative, there is no solution (non-real).

Let’s predict how many solutions a quadratic equation will have and verify.

By this we can see that there will be 1 solution.

Example 2:

As we can see the radical is negative, meaning there’s no real solution. There isn’t really a point in trying to verify since the radical won’t magically change.

Example 3:

The radical is positive, there will be 2 solutions.

If the discriminant isn’t a perfect square, it is usually best to leave the radical as an absolute value. You will still have 2 answers hence the +/- sign.