Given that quadratics can be written as . The discriminant can be found by looking at  or the value under the radical of the quadratic formula. Using substiution and order of operations we can find this value of the discriminant of this quadratic equation.

The discrimiant will determine how many solutions a quadratic has. If the discriminant is positive, then there are two real solutions. If it is negative then there are two immaginary solutions. If it is equal to zero then there is one repeated solution.

Given that quadratics can be written as . The discriminant can be found by looking at  or the value under the radical of the quadratic formula. Using substiution and order of operations we can find this value of the discriminant of this quadratic equation.

The discriminant is positive; therefore, there are two real solutions to this quadratic.

This is using the discriminant to find roots. The discriminant as you recall is

If you get a negative number you have no real roots, if you get zero you have one, and if you get a positive number you have two real roots.

So plug in your numbers:

Because you get a negative number you have zero real roots.

The discriminant is part of the quadratic formula. In the quadratic formula, 

The discriminant is the term:

If the discriminant is 0, there is only one real solution. This would be:

, since the our discriminant is gone.

If the discriminant is a positive number, then we have two real roots, the usual form of the quadratic equation:

Finally, if the discriminant is negative, we would be taking the square root of a negative number. This will give us no real zeros.

Plugging the numbers into the discriminant gives us:

The discriminant is zero, so there is only one root,

Using the discriminant, which for a polynomial 

is equal to

,

we can determine the number of roots a polynomial has. If the discriminant is positive, then the polynomial has two real roots. If it is equal to zero, the polynomial has one real root. If it is negative, then the polynomial has two roots which are complex conjugates of one another.

For our function, we have

,

so when we plug these into the discriminant formula, we get

So, our polynomial has two real roots.

The discriminant is found using the following formula:

For the particular function in question the variable are as follows.

Therefore:

To determine the amount of roots a given quadratic function has, we must find the discriminant, which for 

is equal to

If d is negative, then we have two roots that are complex conjugates of one another. If d is positive, than we have two real roots, and if d is equal to zero, then we have only one real root.

Using our function and the formula above, we get

Thus, the function has only one real root.

Write the formula for the discriminant.  This is the term inside the square root of the quadratic formula.

The given equation is already in the form of .

Substitute the terms into the formula.

The answer is:  

The polynomial is written in the form , where

Write the formula for the discriminant.  This is the term inside the square root value of the quadratic equation.

Substitute all the knowns into this equation.

The answer is:  

We use the quadratic formula to evaluate the types of roots, but it is not necessary to solve the whole equation. Simply look at the discriminant or square root part. 

Plug in the correct numbers in the discriminant and simplify. Do not take the square root.

Since  will be negative, this equation will have two complex solutions.

Discrimant<0= Two complex solutions

Discriminant>0= Two distinct and real solutions

Discriminant=0 = One repeated solution