High School Math : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for High School Math

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Example Questions

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.

Example Question #4 : Finding Roots

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

Factor out a  from the entire equation. After that, you get . Factor the expression to . Set both of those equal to zero and your answers are  and

Example Question #5 : Finding Roots

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

This expression is the difference of perfect squares. Therefore, it factors to. Set both of those equal to zero and your answers are  and .

Example Question #6 : Finding Roots

Find the zeros. 

Possible Answers:

Correct answer:

Explanation:

Factor the equation to . Set both equal to  and you get  and

Example Question #7 : Finding Roots

Find the zeros. 

Possible Answers:

Correct answer:

Explanation:

Factor a  out of the quation to get

 

which can be further factored to

.

Set the last two expressions equal to zero and you get  and

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