You need to first factor the equation. Then you willbe able to set those expressions equal to 0 and find your roots. There is only one way to get your leading coefficient of 3 (3 x 1) so that's helpful when figuring it out.

In the form  remember you want a factor of  that when mulitplied by the factor of  and added together will give you the value of .

 Factored, it comes out to:

.

When you set those expressions equal to 0, you get

.

The roots of a quadratic can be found by factoring. Factoring the solution will give you an expression that when multiplying will result in the initial quadratic.

The roots for this expression are . Similarly the roots of a quadratic can be found using the quadratic quadratic formula where the parent function of a quadratic is represented as  and the quadratic formula is .

Roots when looking at a graph are simply the x-values of where the function crosses the x-axis.

Which, when looking at this graph, it is clearly

  and  

To solve this equation perform the oppisite operation to isolate the variable.

Recall that the square root of a negative number results in an imaginary number.

Therefore,

.

To solve this equation perform the oppisite operation to isolate the variable.

Recall that the square root of a negative number is an imaginary number.

Therefore,

.

The x-intercepts of a quadratic equation are also the solutions. To find them, factor the quadratic equation. After some trial and error, it can be factored to: . Set those expressions equal to  to get you x-intercepts. Your answers are: .

Find all solutions to the following quadratic equation:

We can solve the following equation by first bringing the -225 to the other side:

Next, take the square root of both sides.

Now, you may be tempted to write your answer as just

But, we need to remeber the following is also true

So our answer choice must include both positive and negative 15

To find the roots, or solutions, of the equation, factor the quadratic. It factors to . Then, set each expression equal to 0 to get your roots of 1 and 4.

An x-intercept is the same thing as a root or solution. Therefore, we can set the function equal to 0 and solve for x. .

The first step in finding the root is to factor the polynomial. The common factor in each term is , so extract that from the equation first. . Continue to find the numbers that will multiply to , and add to . If there is no number in front of the variable, it means there is just one of them! 

The factors of . One of the terms will need to be negative, and in this case it will be the larger number in order to equal . The numbers that work are . The factored polynomial would be . There are three roots for this problem. The first will be 0, because if the  is multiplied by , then it will equal 0. The other numbers to fulfill the equation would be . Therefore, the roots are .