# High School Math : Finding Roots

## Example Questions

### Example Question #61 : Intermediate Single Variable Algebra

Solve the following equation by factoring.

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 #32 : Quadratic Equations And Inequalities

Solve the following equation by factoring.

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 #62 : Intermediate Single Variable Algebra

Solve the following equation by factoring.

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 #11 : Finding Roots

Solve

Explanation:

Factor the problem and set each factor equal to zero.

becomes so

### Example Question #71 : Intermediate Single Variable Algebra

Solve .

Explanation:

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

becomes so the correct answer is  .

### Example Question #1611 : High School Math

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 .

Solve .