# High School Math : Understanding the Discriminant

## Example Questions

### Example Question #1 : Understanding The Discriminant

Use the discriminant to determine the nature of the roots:

rational root

imaginary root

rational roots

irrational roots

imaginary roots

irrational roots

Explanation:

The formula for the discriminant is:

Since the discriminant is positive and not a perfect square, there are  irrational roots.

### Example Question #2 : Understanding The Discriminant

Use the discriminant to determine the nature of the roots:

irrational roots

rational roots

imaginary roots

imaginary root

rational root

imaginary roots

Explanation:

The formula for the discriminant is:

Since the discriminant is negative, there are  imaginary roots.

### Example Question #3 : Understanding The Discriminant

Use the discriminant to determine the nature of the roots:

imaginary roots

real root

real roots

Cannot be determined

imaginary root

imaginary roots

Explanation:

The formula for the discriminant is:

Since the discriminant is negative, there are  imaginary roots.

### Example Question #4 : Understanding The Discriminant

Given , what is the value of the discriminant?

Explanation:

In general, the discriminant is .

In this particual case .

Plug in these three values and simplify: