# Algebra II : Quadratic Formula

## Example Questions

### Example Question #321 : Quadratic Equations And Inequalities

Find the roots of .

no real solutions

no real solutions

Explanation:

Since the original equation is in standard form,  where

.

Therefore,

because the value of the discriminant (the component beneath the square root) is negative, this function has no real solutions.

### Example Question #32 : Quadratic Formula

Solve .

No real solutions

No real solutions

Explanation:

This function cannot be factor therefore, use the quadratic equation.

Since the original equation is in the form  where

.

Therefore,

Since the value of the discriminant (the value beneath the square root symbol) is negative, this function has no real solutions.

### Example Question #31 : Quadratic Formula

Solve .

Explanation:

This particular function cannot be factored therefore, use the quadratic formula to solve.

Since the function is in the form  where

the quadratic formula becomes as follows.

### Example Question #34 : Quadratic Formula

Use the quadratic formula to solve for x:

Explanation:

To solve this problem, you must first rewrite the equation into   form (quadratic form).

After this you plug the numbers into the following quadratic equation:

Which upon doing  you get:

This simplifies to:

### Example Question #31 : Quadratic Formula

Explanation:

Recall the general form of a quadratic,

The solution set has the form,

For our particular case, , and

### Example Question #36 : Quadratic Formula

Use the quadratic formula to find the roots of the following equation.

Explanation:

First, simplify the equation, so that the numbers are easier to work with. We can see that we can factor a 2 from each term.

Now we can divide both sides by 2, to further simplify.

Now that we have simplified we can apply the quadratic formula.

where a, b, and c are the constants defined as follows:

This means our a is 1, our b is -6, and our c is 8.

Finally, lets plug the numbers into the formula:

and

or more simply:

These are the roots of the equation.

### Example Question #32 : Quadratic Formula

Find the roots of the equation using the quadratic equation.

Explanation:

where a, b, and c are the constants defined as follows:

This means our a is 1, our b is -6, and our c is 8.

Finally, lets plug the numbers into the formula:

These are the roots of the equation.

Remember that using  is the exact same as writing:

Explanation:

Therefore:

### Example Question #38 : Quadratic Formula

Solve for x:

Explanation:

Using the formula for our function, we get

Notice that we have a negative under the square root. This means that we must use the imaginary number

and our roots will be imaginary.

Simplifying using i, we get

### Example Question #39 : Quadratic Formula

Find the roots using the quadratic formula