### All High School Math Resources

## Example Questions

### Example Question #1 : Simplifying And Expanding Quadratics

Solve the equation for .

**Possible Answers:**

**Correct answer:**

Cross multiply.

Set the equation equal to zero.

Factor to find the roots of the polynomial.

and

### Example Question #1 : Foil

Evaluate

**Possible Answers:**

**Correct answer:**

In order to evaluate one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.

Multiply terms by way of FOIL method.

Now multiply and simplify.

### Example Question #41 : Intermediate Single Variable Algebra

Expand .

**Possible Answers:**

**Correct answer:**

To solve our given equation, we need to use FOIL (First, Outer, Inner, Last).

Combine like terms.

### Example Question #42 : Intermediate Single Variable Algebra

FOIL .

**Possible Answers:**

**Correct answer:**

Remember FOIL stands for First Outer Inner Last.

Combine like terms to get .

### Example Question #1 : Understanding The Discriminant

Use the discriminant to determine the nature of the roots:

**Possible Answers:**

imaginary roots

rational roots

irrational roots

rational root

imaginary root

**Correct answer:**

irrational roots

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:

**Possible Answers:**

irrational roots

rational roots

imaginary root

rational root

imaginary roots

**Correct answer:**

imaginary roots

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:

**Possible Answers:**

imaginary root

real roots

Cannot be determined

imaginary roots

real root

**Correct answer:**

imaginary roots

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?

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

Certified Tutor