# High School Math : Understanding the Discriminant

## Example Questions

### Example Question #1 : Understanding The Discriminant

Use the discriminant to determine the nature of the roots:  imaginary roots rational roots irrational roots rational root imaginary root 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 root rational root imaginary roots 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 root real roots

Cannot be determined imaginary roots real 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?      In general, the discriminant is .
In this particual case .
Plug in these three values and simplify:  