Algebra II : Quadratic Formula

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1641 : Algebra Ii

Determine a root:  

Possible Answers:

Correct answer:

Explanation:

Identify the coefficients given the equation in standard form:

Write the quadratic formula.

Substitute the coefficients.

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

The answer is:  

Example Question #1642 : Algebra Ii

Determine a possible root for:  

Possible Answers:

Correct answer:

Explanation:

Write the quadratic formula.

Identify and substitute the terms.

Factor the radical using factors of perfect squares.

These two answers are possible roots.

The answer is:  

Example Question #193 : Solving Quadratic Equations

Find the roots of the quadratic function, 

 

 

Where  is any real number constant not equal to zero.

 

 

Possible Answers:

 

 

Correct answer:

 

Explanation:

 

To find the roots set the function to zero: 

 ,

                                                      (1)

 

Apply the quadratic formula:

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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) 

 _____________________________________________________________

 

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, 

Possible Answers:

Correct answer:

Explanation:

 

The roots are the values of  for which: 

 

______________________________________________________________

Reminder

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

                                                         

 _____________________________________________________________

 

 

 

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.

Possible Answers:

Correct answer:

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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