Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : Zeros/Roots of a Polynomial

Study concepts, example questions & explanations for College Algebra

Create An Account

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=- 297x - 270x^{2} - 27\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=1,\frac{1}{10}$

x=540,54

$x=-1,-\frac{1}{10}$

x=-540,-54

Correct answer:

$x=-1,-\frac{1}{10}$

Explanation:

$\begin{align*}&\text{The function }f(x)=- 297x - 270x^{2} - 27\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&-27\cdot (x + 1)\cdot (10x + 1)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-297)\pm\sqrt{(-297)^2-4(-270)(-27)}}{2(-270)}=\frac{297\pm243}{-540}\\&\text{Either way, we find that the function crosses the x-axis at}\ x=-1\text{ and }-\frac{1}{10}.\end{align*}$

Report an Error

Example Question #2 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=- 822x - 288x^{2} - 567\\&\text{has a zero value.}\end{align*}$

Possible Answers:

$x=-\frac{7}{6},-\frac{27}{16}$

x=972,672

$x=\frac{7}{6},\frac{27}{16}$

x=-972,-672

Correct answer:

$x=-\frac{7}{6},-\frac{27}{16}$

Explanation:

$\begin{align*}&\text{Given }f(x)=- 822x - 288x^{2} - 567\text{, to find when it has a value of}\\&\text{zero, we need a method to determine the x values that}\\&\text{make this happen. We can either factor the equation:}\\&-3\cdot (16x + 27)\cdot (6x + 7)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-822)\pm\sqrt{(-822)^2-4(-288)(-567)}}{2(-288)}=\frac{822\pm150}{-576}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=-\frac{7}{6}\text{ and }-\frac{27}{16}.\end{align*}$

Report an Error

Example Question #3 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=- 648x - 152x^{2} - 576\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

x=-912,-384

$x=3,\frac{24}{19}$

$x=-3,-\frac{24}{19}$

x=912,384

Correct answer:

$x=-3,-\frac{24}{19}$

Explanation:

$\begin{align*}&\text{The function }f(x)=- 648x - 152x^{2} - 576\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&-8\cdot (x + 3)\cdot (19x + 24)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-648)\pm\sqrt{(-648)^2-4(-152)(-576)}}{2(-152)}=\frac{648\pm264}{-304}\\&\text{Either way, we find thatthe function crosses the x-axis at} \ x=-3\text{ and }-\frac{24}{19}.\end{align*}$

Report an Error

Example Question #4 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=712x - 110x^{2} - 728\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=-\frac{26}{5},-\frac{14}{11}$

x=-280,-1144

x=280,1144

$x=\frac{26}{5},\frac{14}{11}$

Correct answer:

$x=\frac{26}{5},\frac{14}{11}$

Explanation:

$\begin{align*}&\text{The function }f(x)=712x - 110x^{2} - 728\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&-2\cdot (11x - 14)\cdot (5x - 26)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(712)\pm\sqrt{(712)^2-4(-110)(-728)}}{2(-110)}=\frac{-712\pm432}{-220}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{26}{5}\text{ and }\frac{14}{11}.\end{align*}$

Report an Error

Example Question #1 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=- 544x - 152x^{2} - 480\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=2,\frac{30}{19}$

x=608,480

$x=-2,-\frac{30}{19}$

x=-608,-480

Correct answer:

$x=-2,-\frac{30}{19}$

Explanation:

$\begin{align*}&\text{The function }f(x)=- 544x - 152x^{2} - 480\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&-8\cdot (x + 2)\cdot (19x + 30)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-544)\pm\sqrt{(-544)^2-4(-152)(-480)}}{2(-152)}=\frac{544\pm64}{-304}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=-2\text{ and }-\frac{30}{19}.\end{align*}$

Report an Error

Example Question #6 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=225x^{2} - 623x + 374\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

x=850,396

$x=\frac{22}{25},\frac{17}{9}$

$x=-\frac{22}{25},-\frac{17}{9}$

x=-850,-396

Correct answer:

$x=\frac{22}{25},\frac{17}{9}$

Explanation:

$\begin{align*}&\text{The function }f(x)=225x^{2} - 623x + 374\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&(25x - 22)\cdot (9x - 17)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-623)\pm\sqrt{(-623)^2-4(225)(374)}}{2(225)}=\frac{623\pm227}{450}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{22}{25}\text{ and }\frac{17}{9}.\end{align*}$

Report an Error

Example Question #1 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=108x^{2} - 60x - 25\\&\text{has a zero value.}\end{align*}$

Possible Answers:

x=180,-60

$x=-\frac{5}{6},-\frac{5}{18}$

$x=\frac{5}{6},-\frac{5}{18}$

$x=-\frac{5}{6},\frac{5}{18}$

Correct answer:

$x=\frac{5}{6},-\frac{5}{18}$

Explanation:

$\begin{align*}&\text{Given }f(x)=108x^{2} - 60x - 25\text{, to find when it has a value of}\\&\text{zero, we need a method to determine the x values that}\\&\text{make this happen. We can either factor the equation:}\\&(18x + 5)\cdot (6x - 5)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-60)\pm\sqrt{(-60)^2-4(108)(-25)}}{2(108)}=\frac{60\pm120}{216}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{5}{6}\text{ and }-\frac{5}{18}.\end{align*}$

Report an Error

Example Question #8 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=421x + 306x^{2} - 210\\&\text{has a zero value.}\end{align*}$

Possible Answers:

$x=\frac{7}{18},-\frac{30}{17}$

$x=-\frac{7}{18},\frac{30}{17}$

x=238,-1080

x=-238,1080

Correct answer:

$x=\frac{7}{18},-\frac{30}{17}$

Explanation:

$\begin{align*}&\text{Given }f(x)=421x + 306x^{2} - 210\text{, to find when it has a value of}\\&\text{zero, we need a method to determine the x values that}\\&\text{make this happen. We can either factor the equation:}\\&(17x + 30)\cdot (18x - 7)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(421)\pm\sqrt{(421)^2-4(306)(-210)}}{2(306)}=\frac{-421\pm659}{612}\\&\text{Either way, we find thatthe function crosses the x-axis at} \ x=\frac{7}{18}\text{ and }-\frac{30}{17}.\end{align*}$

Report an Error

Example Question #9 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=323x + 29x^{2} - 300\\&\text{has a zero value.}\end{align*}$

Possible Answers:

x=50,-696

x=-50,696

$x=-12,\frac{25}{29}$

$x=12,-\frac{25}{29}$

Correct answer:

$x=-12,\frac{25}{29}$

Explanation:

$\begin{align*}&\text{Given }f(x)=323x + 29x^{2} - 300\text{, to find when it has a value of}\\&\text{zero, we need a method to determine the x values that}\\&\text{make this happen. We can either factor the equation:}\\&(x + 12)\cdot (29x - 25)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(323)\pm\sqrt{(323)^2-4(29)(-300)}}{2(29)}=\frac{-323\pm373}{58}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=-12\text{ and }\frac{25}{29}.\end{align*}$

Report an Error

Example Question #10 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the root(s) the function: }f(x)=379x + 276x^{2} - 696\end{align*}$

Possible Answers:

x=576,-1334

$x=-\frac{24}{23},\frac{29}{12}$

x=-576,1334

$x=\frac{24}{23},-\frac{29}{12}$

Correct answer:

$x=\frac{24}{23},-\frac{29}{12}$

Explanation:

$\begin{align*}&\text{The roots of the function }f(x)=379x + 276x^{2} - 696\text{ are the x values}\\&\text{that give it a value of zero. To find these x values}\\&\text{we can either factor the equation:}\\&(12x + 29)\cdot (23x - 24)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(379)\pm\sqrt{(379)^2-4(276)(-696)}}{2(276)}=\frac{-379\pm955}{552}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{24}{23}\text{ and }-\frac{29}{12}.\end{align*}$

Report an Error

View College Algebra Tutors

Yuliya
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Mathematics. George Washington University, Masters in Education, Ed...

View College Algebra Tutors

Sanford
Certified Tutor

Westminster College, Bachelor of Science, Social Studies Teacher Education.

View College Algebra Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Atlanta, ISEE Tutors in Dallas Fort Worth, GMAT Tutors in Denver, Calculus Tutors in San Francisco-Bay Area, Math Tutors in Chicago, Biology Tutors in Phoenix, ACT Tutors in Seattle, French Tutors in Washington DC, Chemistry Tutors in New York City, GRE Tutors in Denver

Popular Courses & Classes

ISEE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Phoenix, ACT Courses & Classes in Boston, GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in Chicago, LSAT Courses & Classes in Denver, SSAT Courses & Classes in Miami, ISEE Courses & Classes in Philadelphia, GRE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Houston

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Houston, SAT Test Prep in Chicago, SSAT Test Prep in Los Angeles, ISEE Test Prep in Dallas Fort Worth, GMAT Test Prep in San Diego, SAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Houston, GRE Test Prep in Denver, GMAT Test Prep in Atlanta

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

College Algebra : Zeros/Roots of a Polynomial

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #1 : Zeros/Roots Of A Polynomial

Example Question #2 : Zeros/Roots Of A Polynomial

Example Question #3 : Zeros/Roots Of A Polynomial

Example Question #4 : Zeros/Roots Of A Polynomial

Example Question #1 : Zeros/Roots Of A Polynomial

Example Question #6 : Zeros/Roots Of A Polynomial

Example Question #1 : Zeros/Roots Of A Polynomial

Example Question #8 : Zeros/Roots Of A Polynomial

Example Question #9 : Zeros/Roots Of A Polynomial

Example Question #10 : Zeros/Roots Of A Polynomial

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: