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 #1 : Quadratic Roots

Give the solution set of the equation $x ^{2} + 4x -17 = 0$ .

Possible Answers:

$x = 2 \pm i \sqrt{13}$

$x = -2 \pm i \sqrt{21}$

$x = 2 \pm \sqrt{13}$

$x = -2 \pm i \sqrt{13}$

$x = -2 \pm \sqrt{21}$

Correct answer:

$x = -2 \pm \sqrt{21}$

Explanation:

Using the quadratic formula, with a = 1, b = 4, c = -17 :

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

$x = \frac{-(4) \pm \sqrt{(4)^{2}-4 (1)(-17)}}{2 (1)}$

$x = \frac{-4 \pm \sqrt{16-(-68)}}{2 }$

$x = \frac{-4 \pm \sqrt{84}}{2 }$

$x = \frac{-4 \pm \sqrt{4} \cdot \sqrt{21}}{2 }$

$x = \frac{-4 \pm 2 \sqrt{21}}{2 }$

$x = -2 \pm \sqrt{21}$

Report an Error

Example Question #1 : Quadratic Roots

Give the solution set of the equation $x ^{2} + 4x + 13= 0$ .

Possible Answers:

$x = 2 \pm 3 i$

$x = -2 \pm 3 i$

$x = -5 \textup{ or } x= 1$

$x = -3 \pm 2i$

$x = -1 \textup{ or } x= 5$

Correct answer:

$x = -2 \pm 3 i$

Explanation:

Using the quadratic formula, with a = 1, b = 4, c = 13 :

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

$x = \frac{-(4) \pm \sqrt{(4)^{2}-4 (1)(13)}}{2 (1)}$

$x = \frac{-4 \pm \sqrt{16-52}}{2 }$

$x = \frac{-4 \pm \sqrt{-36}}{2 }$

$x = \frac{-4 \pm i \sqrt{36}}{2 }$

$x = \frac{-4 \pm 6 i }{2 }$

$x = -2 \pm 3 i$

Report an Error

Example Question #2 : Quadratic Roots

Write a quadratic equation in the form ax^2+bx+c=0 with 2 and -10 as its roots.

Possible Answers:

x^2+2x-10=0

x^2+8x-10=0

x^2+10x-2=0

x^2+12x-20=0

x^2+8x-20=0

Correct answer:

x^2+8x-20=0

Explanation:

Write in the form (x-p)(x-q)=0 where p and q are the roots.

Substitute in the roots:

(x-2)(x-(-10))=0

Simplify:

(x-2)(x+10)=0

Use FOIL and simplify to get

x^2+8x-20=0 .

Report an Error

Example Question #4 : Quadratic Roots

Find the roots of the following quadratic polynomial:

6x^2+2x-28

Possible Answers:

$-4, \frac{7}{6}$

$2, -\frac{7}{3}$

$\frac{3}{4},-\frac{2}7{}$

This quadratic has no real roots.

$\frac{3}{14},1$

Correct answer:

$2, -\frac{7}{3}$

Explanation:

To find the roots of this equation, we need to find which values of make the polynomial equal zero; we do this by factoring. Factoring is a lot of "guess and check" work, but we can figure some things out. If our binomials are in the form (ax+b)(cx+d) , we know times will be and times will be . With that in mind, we can factor our polynomial to

(2x-4)(3x+7)

To find the roots, we need to find the -values that make each of our binomials equal zero. For the first one it is , and for the second it is $-\frac{7}{3}$ , so our roots are $2, -\frac{7}{3}$ .

Report an Error

Example Question #143 : Understanding Quadratic Equations

Write a quadratic equation in the form $ax^{2}+bx+c=0$ that has and as its roots.

Possible Answers:

$x^{2}+12x+32=0$

$x^{2}-4x-32=0$

$x^{2}+8x+1=0$

$x^{2}+4x-32=0$

$x^{2}-12x+32=0$

Correct answer:

$x^{2}+4x-32=0$

Explanation:

1. Write the equation in the form (x-a)(x-b)=0 where and are the given roots.

(x-4)(x-(-8))=0

(x-4)(x+8)=0

2. Simplify using FOIL method.

$x^{2}+4x-32=0$

Report an Error

Example Question #311 : Intermediate Single Variable Algebra

Give the solution set of the following equation:

$x^{2}+3x+3=0$

Possible Answers:

$x=\frac{3\pm i\sqrt{2}}{2}$

$x={-3\pm i\sqrt{3}}$

$x=\frac{-3\pm i\sqrt{3}}{2}$

$x=\frac{3\pm \sqrt{3}}{2}$

$x=\frac{-6\pm i\sqrt{-3}}{2}$

Correct answer:

$x=\frac{-3\pm i\sqrt{3}}{2}$

Explanation:

Use the quadratic formula with a=1 , b=3 and c=3 :

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

$x=\frac{-3\pm \sqrt{3^{2}-4(1)(3)}}{2(1)}$

$x=\frac{-3\pm \sqrt{9-12}}{2}$

$x=\frac{-3\pm \sqrt{-3}}{2}$

$x=\frac{-3\pm i\sqrt{3}}{2}$

Report an Error

Example Question #1 : Quadratic Roots

Give the solution set of the following equation:

$10x^{2}+4x+5=0$

Possible Answers:

$x=\frac{-4\pm \sqrt {184}}{10}$

$x=\frac{-4\pm i\sqrt {46}}{20}$

$x=\frac{-2\pm \sqrt {46}}{20}$

$x=\frac{-2\pm i\sqrt {46}}{10}$

$x=\frac{-4\pm i\sqrt {46}}{10}$

Correct answer:

$x=\frac{-2\pm i\sqrt {46}}{10}$

Explanation:

Use the quadratic formula with a=10 , b=4 , and c=5 :

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

$x=\frac{-4\pm \sqrt{4^{2}-4(10)(5)}}{2(10)}$

$x=\frac{-4\pm \sqrt{16-200}}{20}$

$x=\frac{-4\pm \sqrt{-184}}{20}$

$x=\frac{-4\pm \sqrt{46\cdot 4\cdot -1}}{20}$

$x=\frac{-4\pm 2i\sqrt{46}}{20}$

$x=\frac{-2\pm i\sqrt{46}}{10}$

Report an Error

Example Question #144 : Understanding Quadratic Equations

Let

(x-3)^2 = 36

Determine the value of x.

Possible Answers:

x=6,-6

x=6

x=-3, 9

x=9

Correct answer:

x=-3, 9

Explanation:

To solve for x we need to isolate x. We can do this by taking the square root of each side and then doing algebraic operations.

(x-3)^2=36

$\sqrt(x-3)^2=\sqrt36$

$x-3=\pm6$

Now we need to separate our equation in two and solve for each x.

x-3=6 or x-3=-6

x=9 x=-3

Report an Error

Example Question #151 : Understanding Quadratic Equations

Solve for :

$(x-3)^{2}=36$

Possible Answers:

(9,3)

(9,-3)

None of the other answers

(6,-6)

(3,-9)

Correct answer:

(9,-3)

Explanation:

To solve this equation, you must first eliminate the exponent from the (x-3) by taking the square root of both sides:

$\sqrt{(x-3)^{2}}=\sqrt{36}$

Since the square root of 36 could be either or , there must be 2 values of . So, solve for

x-3=-6

and

x-3=6

to get solutions of (9,-3) .

Report an Error

Example Question #1 : Quadratic Roots

Find the roots of $y = x^{2} + 9x + 14$ .

Possible Answers:

x = 4, x = 5

x=0

x = 7, x = 2

x = -7, x = -2

x = 14, x = 1

Correct answer:

x = -7, x = -2

Explanation:

When we factor, we are looking for two number that multiply to the constant, , and add to the middle term, . Looking through the factors of , we can find those factors to be and .

Thus, we have the factors:

(x + 2)(x+7) .

To solve for the solutions, set each of these factors equal to zero.

Thus, we get x + 2 = 0 , or x = -2 .

Our second solution is, x + 7 =0 , or x = -7 .

Report an Error

View Algebra 2 Tutors

Shakeel
Certified Tutor

View Algebra 2 Tutors

Evgenii
Certified Tutor

View Algebra 2 Tutors

Joseph
Certified Tutor

Rutgers University-New Brunswick, Bachelor in Arts, Chemistry. Rutgers Graduate School of Biomedical Sciences, Current Grad S...

All Algebra II Resources

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

Popular Subjects

Reading Tutors in Atlanta, Spanish Tutors in Washington DC, Physics Tutors in Atlanta, Chemistry Tutors in Boston, MCAT Tutors in Philadelphia, LSAT Tutors in Seattle, Spanish Tutors in Miami, GMAT Tutors in Atlanta, GMAT Tutors in San Francisco-Bay Area, Physics Tutors in Houston

Popular Courses & Classes

GRE Courses & Classes in San Diego, SAT Courses & Classes in San Diego, LSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Los Angeles, GRE Courses & Classes in Boston, GMAT Courses & Classes in Philadelphia, SAT Courses & Classes in Phoenix, ISEE Courses & Classes in Phoenix, MCAT Courses & Classes in Houston, SAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

MCAT Test Prep in Los Angeles, ISEE Test Prep in Atlanta, SAT Test Prep in Seattle, GMAT Test Prep in Denver, LSAT Test Prep in Boston, GRE Test Prep in Seattle, MCAT Test Prep in Washington DC, GRE Test Prep in Los Angeles, GRE Test Prep in Chicago, SSAT Test Prep in New York City

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 #1 : Quadratic Roots

Example Question #1 : Quadratic Roots

Example Question #2 : Quadratic Roots

Example Question #4 : Quadratic Roots

Example Question #143 : Understanding Quadratic Equations

Example Question #311 : Intermediate Single Variable Algebra

Example Question #1 : Quadratic Roots

Example Question #144 : Understanding Quadratic Equations

Example Question #151 : Understanding Quadratic Equations

Example Question #1 : Quadratic Roots

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: