# 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 root imaginary roots rational root rational roots irrational 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 #42 : Intermediate Single Variable Algebra

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

Explanation:

The formula for the discriminant is:   Since the discriminant is negative, there are imaginary roots.

### Example Question #1 : Understanding The Discriminant

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

Cannot be determined real root imaginary roots

Explanation:

The formula for the discriminant is:   Since the discriminant is negative, there are imaginary roots.

### Example Question #1 : Discriminants

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: ### All High School Math Resources 