# High School Math : Intermediate Single-Variable Algebra

## Example Questions

### 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?

Explanation:

In general, the discriminant is .

In this particual case .

Plug in these three values and simplify:

### Example Question #1 : Understanding Quadratic Roots

Write an equation with the given roots:

Explanation:

To write an equation, find the sum and product of the roots. The sum is the negative coefficient of , and the product is the integer.

Sum:

Product:

Subtract the sum and add the product.

The equation is:

Multiply the equation by :

### Example Question #2 : Understanding Quadratic Roots

Write an equation with the given roots:

Explanation:

To write an equation, find the sum and product of the roots. The sum is the negative coefficient of , and the product is the integer.

Sum:

Product:

Subtract the sum and add the product.

The equation is:

### Example Question #3 : Understanding Quadratic Roots

Write an equation with the given roots:

Explanation:

To write an equation, find the sum and product of the roots. The sum is the negative coefficient of , and the product is the integer.

Sum:

Product:

Subtract the sum and add the product.

The equation is:

### Example Question #4 : Understanding Quadratic Roots

Write an equation with the given roots:

Explanation:

To write an equation, find the sum and product of the roots. The sum is the negative coefficient of , and the product is the integer.

Sum:

Product:

Subtract the sum and add the product.

The equation is:

Multiply the equation by :

### Example Question #5 : Understanding Quadratic Roots

Write an equation with the given roots:

Explanation:

To write an equation, find the sum and product of the roots. The sum is the negative coefficient of , and the product is the integer.

Sum:

Product:

Subtract the sum and add the product.

The equation is:

### Example Question #1 : Finding Roots

Find the zeros.

Explanation:

Factor the equation to . Set both equal to zero and you get  and . Remember, the zeros of an equation are wherever the function crosses the -axis.

### Example Question #2 : Finding Roots

Find the zeros.

Explanation:

Factor out an  from the equation so that you have . Set  and  equal to . Your roots are  and .

Find the zeros.