High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

varsity tutors app store varsity tutors android store

Example Questions

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

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?

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

Explanation:

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

Example Question #3 : Finding Roots

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

Set  equal to zero and you get . Set  equal to zero as well and you get  and  because when you take a square root, your answer will be positive and negative.

Learning Tools by Varsity Tutors