### All High School Math Resources

## Example Questions

### Example Question #11 : Solving Quadratic Equations

Solve the following equation by factoring.

**Possible Answers:**

**Correct answer:**

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:**

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:**

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:**

Factor the problem and set each factor equal to zero.

becomes so

### Example Question #15 : Solving Quadratic Equations

Solve .

**Possible Answers:**

**Correct answer:**

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:**

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:**

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 .

### Example Question #41 : Quadratic Equations And Inequalities

What are the roots of ?

**Possible Answers:**

**Correct answer:**

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:**

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:**

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 .

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