High School Math : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #41 : Quadratic Equations And Inequalities

What are the roots of ?

Possible Answers:

Correct answer:

Explanation:

To find the roots, we need to find what would make . Since there are two parts to , we will have two roots: one where , and one where .

Solve each individually.

Therefore, our two roots will be at .

Example Question #42 : Quadratic Equations And Inequalities

Solve .

Possible Answers:

No solutions

Correct answer:

Explanation:

Factor the equation by looking for two factors that multiply to and add to .

The factors are and , so the equation to solve becomes .

Next, set each factor equal to zero and solve:

 or

The solution is or .

Example Question #43 : Quadratic Equations And Inequalities

Solve .

 

Possible Answers:

Correct answer:

Explanation:

To find the roots of this equation, you can factor it to 

Set each of those expressions equal to zero and then solve for . The roots are  and 

Example Question #44 : Quadratic Equations And Inequalities

Find the root(s) of the following quadratic polynomial. 

Possible Answers:

Correct answer:

Explanation:

We set the function equal to 0 and factor the equation. By FOIL, we can confirm that  is equivalent to the given function. Thus, the only zero comes from, and . Thus,  is the only root. 

Example Question #45 : Quadratic Equations And Inequalities

Possible Answers:

Correct answer:

Explanation:

Example Question #46 : Quadratic Equations And Inequalities

Solve the quadratic equation using any method:

Possible Answers:

Correct answer:

Explanation:

Use the quadratic formula to solve:

Example Question #47 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

Possible Answers:

Correct answer:

Explanation:

Factor and solve:

or

This has no solutions.

Therefore there is only one solution:

Example Question #48 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

Possible Answers:

Correct answer:

Explanation:

Factor and solve:

or

Therefore the equation has four solutions:

Example Question #49 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

Possible Answers:

Correct answer:

Explanation:

Factor and solve:

or

Therefore the equation has two solutions.

Example Question #50 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

Possible Answers:

Correct answer:

Explanation:

Factor and solve:

Each of these factors gives solutions to the equation:

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