# High School Math : Intermediate Single-Variable Algebra

## Example Questions

### Example Question #14 : Solving Quadratic Equations

Solve

Explanation:

Factor the problem and set each factor equal to zero.

becomes so

### Example Question #15 : Solving Quadratic Equations

Solve .

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 ?

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 ?

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 .

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

What are the roots of ?

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 .

No solutions

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 .

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.

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.

Explanation:

### Example Question #46 : Quadratic Equations And Inequalities

Solve the quadratic equation using any method:

Explanation:

Use the quadratic formula to solve: