High School Math : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #8 : Finding Roots

Find the zeros. 

Possible Answers:

Correct answer:

Explanation:

Set each expression equal to zero and you get 0 and 6.

Example Question #9 : Finding Roots

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

Set both expressions equal to . The first factor yields . The second factor gives you .

Example Question #10 : Finding Roots

Find the zeros. 

Possible Answers:

Correct answer:

Explanation:

Set both expressions to  and you get  and .

Example Question #11 : Solving Quadratic Equations

Solve the following equation by factoring.

Possible Answers:

Correct answer:

Explanation:

We can factor by determining the terms that will multiply to –8 and add to +7.

Our factors are +8 and –1.

Now we can set each factor equal to zero and solve for the root.

Example Question #12 : Solving Quadratic Equations

Solve the following equation by factoring.

Possible Answers:

Correct answer:

Explanation:

We know that one  term has a coefficient of 2 and that our factors must multiply to –10.

Our factors are +2 and –5.

Now we can set each factor equal to zero and solve for the root.

Example Question #13 : Solving Quadratic Equations

Solve the following equation by factoring.

Possible Answers:

Correct answer:

Explanation:

First, we can factor an term out of all of the values.

We can factor remaining polynomial by determining the terms that will multiply to +4 and add to +4.

Our factors are +2 and +2.

Now we can set each factor equal to zero and solve for the root.

Example Question #14 : Solving Quadratic Equations

Solve

Possible Answers:

Correct answer:

Explanation:

Factor the problem and set each factor equal to zero.

becomes so

Example Question #15 : Solving Quadratic Equations

Solve .

Possible Answers:

Correct answer:

Explanation:

Factor the quadratic equation and set each factor equal to zero:

becomes so the correct answer is  .

Example Question #16 : Solving Quadratic Equations

What are the roots of ?

Possible Answers:

Correct answer:

Explanation:

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

Solve each one individually:

 

Therefore, our roots will be .

Example Question #17 : Solving Quadratic Equations

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.

Our two roots will be .

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