Solving Quadratic Equations - Math

Factor the equation to . Set both equal to zero and you get and . Remember, the zeros of an equation are wherever the function crosses the -axis.

Factor out an from the equation so that you have . Set and equal to . Your roots are and .

Set equal to zero and you get . Set equal to zero as well and you get and because when you take a square root, your answer will be positive and negative.

Factor out a from the entire equation. After that, you get . Factor the expression to . Set both of those equal to zero and your answers are and .

This expression is the difference of perfect squares. Therefore, it factors to. Set both of those equal to zero and your answers are and .

Factor the equation to . Set both equal to and you get and .

Factor a out of the quation to get

which can be further factored to

.

Set the last two expressions equal to zero and you get and .

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

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

Set both expressions to and you get and .

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.

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.

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.

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 .

Factor the problem and set each factor equal to zero.

becomes so

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

becomes so the correct answer is .

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 .

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 .