There are multiple methods to solve quadratics. Use whichever is easiest for the problem.

Solve by factoring:

What numbers will multiply to get  and what two numbers will multiply to get -14?

To solve for the roots, set the factors equal to 0 and solve:

To find the roots, or solutions, of this quadratic equation, first factor it.

Recall that when a function is in the  form, the factors of a and c when multiplied and added together must equal b.

First, identify factors of 6 that could equal -1. Y

ou have to think of your positive and negative signs here. Remember that  and you need to have one positive and one negative number to get -6.

Therefore, after factoring, you should get: 

.

Then, set each of those expressions equal to 0.

Therefore, your roots are:

.

Since this function is already factored and equal to 0, you can just set each expression equal to 0 to get your roots.

and

.

The equation will need to be simplified to its standard form.

Simplify this equation by using the FOIL method to expand .

Simplify the terms.

The equation becomes:

Distribute the negative two through the parentheses.

Combine like terms.

The equation in standard for becomes:  

The standard form for a polynomial is:  

Write the quadratic equation.

Substitute the coefficients corresponding to the equation in standard form.

Simplify the radical.  The roots will be imaginary.

Simplify the fractions and replace  with .

The answer is:  

You can solve this quadratic in many different ways, including by graphing or using the quadratic formula. This particular quadratic can be factored:

we're looking for 2 numbers that add to 5 and multiply to

The numbers that work are 8 and -3:

continue factoring

The factors are and . Set each factor equal to zero:

You can solve this quadratic equation in many different ways, including by graphing or factoring. You can also use the quadratic formula:

This will give us two answers:

This quadratic equation can be solved in several ways, including the quadratic equation or by graphing. It can also be solved by factoring:

For this quadratic, we are looking for 2 numbers that add to -19 and multiply to 6x10=60. The numbers satisfying these conditions are -4 and -15:

continue factoring

The factors are and . Set each equal to zero:

This quadratic can be solved in several different ways, including by graphing or factoring. You can also use the quadratic formula:

This gives us two answers:

Use the quadratic equation to determine roots of a parabolic function.

The quadratic formula is:

The equation  in the form of .

Substitute the known coefficients.

Simplify the equation.

The fraction can be broken into two.

Either  or  is a possible root.

The answer is: 

Simplify the equation by dividing by 2:

Find the roots using the quadratic equation:

*Because the discriminant (part under the radical) comes to 0, we know our quadratic will have just one repeated solution.