# Algebra II : Quadratic Formula

## Example Questions

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### Example Question #1641 : Algebra Ii

Determine a root:

Explanation:

Identify the coefficients given the equation in standard form:

Substitute the coefficients.

These two roots are complex and either is a valid answer.

### Example Question #1642 : Algebra Ii

Determine a possible root for:

Explanation:

Identify and substitute the terms.

Factor the radical using factors of perfect squares.

These two answers are possible roots.

### Example Question #193 : Solving Quadratic Equations

Find the roots of the quadratic function,

Where  is any real number constant not equal to zero.

Explanation:

To find the roots set the function to zero:

,

(1)

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Reminder

Recall that for a quadratic   the general formula for the solution in terms of the constant coefficients is given by:

(2)

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Use equation (2) to write a solution for equation (1).

If we simplify the right-hand term in the numerator we obtain:

So now we have for

After all the cancellations in the expression above we obtain:

Therefore, the solution set for this equation is:

### Example Question #194 : Solving Quadratic Equations

Find the roots of the quadratic function,

Explanation:

The roots are the values of  for which:

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Reminder

Recall that for a quadratic   the general formula for the solution in terms of the constant coefficients is given by:

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Use the quadratic formula to find the roots.

Notice that  is not a real number, and therefore the roots will be complex numbers.

Using the definition of the imaginary unit  we can rewrite  as follows,

Now we can write the solutions to this problem in the form:

### Example Question #193 : Solving Quadratic Equations

Find the roots using the quadratic formula.

Explanation:

For this problem

a=1, coefficient of x^2 term

b=9, the coefficient of the x term

c=15, the constant term

solving the expression shows the roots of -6.79 and -2.21

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