High School Math : Understanding Quadratic Equations

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Simplifying And Expanding Quadratics

Solve the equation for .

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

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

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:

Possible Answers:

 irrational roots

 rational roots

 imaginary root

 rational root

 imaginary roots

Correct answer:

 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:

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:

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