Finding Roots

Multiply both sides of the equation by , to get

This can be factored into the form

So we must solve

and

to get the solutions.

The solutions are:

and their sum is .

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.

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.

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

becomes so the correct answer is .

Use the quadratic formula to solve:

Factor and solve:

or

This has no solutions.

Therefore there is only one solution:

Factor and solve:

or

Therefore the equation has four solutions:

Factor and solve:

or

Therefore the equation has two solutions.

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