We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Quadratic Roots

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Quadratic Roots

Write a quadratic function in standard form with roots of -1 and 2.

Possible Answers:

f(x)=x^2-3x-2

f(x)=x^2-x+2

f(x)=x^2-2x-2

f(x)=x^2-x-2

f(x)=x^2+x-2

Correct answer:

f(x)=x^2-x-2

Explanation:

From the zeroes we know

f(x) = (x+1)(x-2)

Use FOIL method to obtain:

f(x)=x^2-x-2

Report an Error

Example Question #312 : Intermediate Single Variable Algebra

Select the quadratic equation that has these roots:

(2x+5)(x-2)

Possible Answers:

2x^2+x-10

2x^2+x+10

2x^2-x+10

None of these.

2x^2-x-10

Correct answer:

2x^2+x-10

Explanation:

(2x+5)(x-2)

FOIL the two factors to find the quadratic equation.

First terms:

$2x\cdot x=2x^2$

Outer terms:

$2x\cdot -2=-4x$

Inner terms:

$5\cdot x=5x$

Last terms:

$5\cdot -2=-10$

Simplify:

2x^2-4x+5x-10

$\boldsymbol{2x^2+x-10}$

Report an Error

Example Question #313 : Intermediate Single Variable Algebra

Solve for a possible root: y=3x^2-6x+8

Possible Answers:

$1-\frac{\sqrt{25}}{2}$

6+6i

$1-\frac{4i\sqrt{3}}{3}$

$1-\frac{i\sqrt{15}}{3}$

$\textup{There are no possible roots.}$

Correct answer:

$1-\frac{i\sqrt{15}}{3}$

Explanation:

Write the quadratic equation.

$x= \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

The equation y=3x^2-6x+8 is in the form y=ax^2+bx+c .

Substitute the proper coefficients into the quadratic equation.

$x= \frac{-(-6)\pm\sqrt{(-6)^2-4(3)(8)}}{2(3)}=\frac{6\pm\sqrt{36-96}}{6}$

$x=\frac{6\pm\sqrt{36-96}}{6} =\frac{6\pm\sqrt{-60}}{6}$

The negative square root can be replaced by the imaginary term . Simplify square root 60 by common factors of numbers with perfect squares.

$\frac{6\pm\sqrt{-60}}{6} = \frac{6\pm i\sqrt{60}}{6} =\frac{6\pm i\sqrt{4} \cdot \sqrt{15}}{6} =\frac{6\pm 2i\sqrt{15}}{6}$

Simplify the fraction.

$\frac{6\pm 2i\sqrt{15}}{6} = 1\pm \frac{i\sqrt{15}}{3}$

A possible root is: $1-\frac{i\sqrt{15}}{3}$

Report an Error

Example Question #1455 : Algebra Ii

Solve for the roots (if any) of y=-8x^2+28x-12

Possible Answers:

$-\frac{1}{2},3$

$\textup{There are no real roots.}$

$\frac{1}{2},3$

$\frac{1}{2},\frac{5}{2}$

$-\frac{1}{4},5$

Correct answer:

$\frac{1}{2},3$

Explanation:

Pull out a common factor of negative four.

y=-4(2x^2-7x+3)

The term inside the parentheses can be factored.

2x^2-7x+3 = (2x-1)(x-3)

Set the binomials equal to zero and solve for the roots. We can ignore the negative four coefficient.

$2x-1=0, x=\frac{1}{2}$

x-3=0, x=3

The answers are: $\frac{1}{2},3$

Report an Error

View Algebra 2 Tutors

Michelle
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mathematics.

View Algebra 2 Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in San Francisco-Bay Area, SAT Tutors in Washington DC, Reading Tutors in San Francisco-Bay Area, Math Tutors in Dallas Fort Worth, GRE Tutors in Los Angeles, Calculus Tutors in Denver, Calculus Tutors in New York City, SAT Tutors in San Francisco-Bay Area, MCAT Tutors in Los Angeles, GMAT Tutors in Dallas Fort Worth

Popular Courses & Classes

ACT Courses & Classes in Boston, SSAT Courses & Classes in Houston, LSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Chicago, Spanish Courses & Classes in San Diego, ACT Courses & Classes in Chicago, GMAT Courses & Classes in San Diego, ISEE Courses & Classes in Houston, MCAT Courses & Classes in Miami, GMAT Courses & Classes in Denver

Popular Test Prep

GMAT Test Prep in Denver, SAT Test Prep in Houston, MCAT Test Prep in Phoenix, GMAT Test Prep in Phoenix, SSAT Test Prep in Philadelphia, SSAT Test Prep in Boston, LSAT Test Prep in Denver, ACT Test Prep in Miami, GMAT Test Prep in Philadelphia, GMAT Test Prep in Chicago

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Quadratic Roots

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #11 : Quadratic Roots

Example Question #312 : Intermediate Single Variable Algebra

Example Question #313 : Intermediate Single Variable Algebra

Example Question #1455 : Algebra Ii

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: