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 #31 : Polynomial Functions

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=360x^{2} - 510x + 130\\&\text{has a zero value.}\end{align*}$

Possible Answers:

$x=-\frac{1}{3},-\frac{13}{12}$

x=780,240

x=-780,-240

$x=\frac{1}{3},\frac{13}{12}$

Correct answer:

$x=\frac{1}{3},\frac{13}{12}$

Explanation:

$\begin{align*}&\text{Given }f(x)=360x^{2} - 510x + 130\text{, to find when it has a value of}\\&\text{zero, we need a method to determine the x values that}\\&\text{make this happen. We can either factor the equation:}\\&10\cdot (3x - 1)\cdot (12x - 13)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-510)\pm\sqrt{(-510)^2-4(360)(130)}}{2(360)}=\frac{510\pm270}{720}\\&\text{Either way, we find thatthe function crosses the x-axis at} \ x=\frac{1}{3}\text{ and }\frac{13}{12}.\end{align*}$

Report an Error

Example Question #32 : Polynomial Functions

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=360x - 250x^{2} + 64\\&\text{has a zero value.}\end{align*}$

Possible Answers:

x=-80,800

x=80,-800

$x=-\frac{8}{5},\frac{4}{25}$

$x=\frac{8}{5},-\frac{4}{25}$

Correct answer:

$x=\frac{8}{5},-\frac{4}{25}$

Explanation:

$\begin{align*}&\text{Given }f(x)=360x - 250x^{2} + 64\text{, to find when it has a value of}\\&\text{zero, we need a method to determine the x values that}\\&\text{make this happen. We can either factor the equation:}\\&-2\cdot (25x + 4)\cdot (5x - 8)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(360)\pm\sqrt{(360)^2-4(-250)(64)}}{2(-250)}=\frac{-360\pm440}{-500}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{8}{5}\text{ and }-\frac{4}{25}.\end{align*}$

Report an Error

Example Question #32 : Polynomial Functions

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=322x^{2} - 325x + 75\\&\text{has a zero value.}\end{align*}$

Possible Answers:

$x=\frac{5}{14},\frac{15}{23}$

$x=-\frac{5}{14},-\frac{15}{23}$

x=420,230

x=-420,-230

Correct answer:

$x=\frac{5}{14},\frac{15}{23}$

Explanation:

$\begin{align*}&\text{Given }f(x)=322x^{2} - 325x + 75\text{, to find when it has a value of}\\&\text{zero, we need a method to determine the x values that}\\&\text{make this happen. We can either factor the equation:}\\&(14x - 5)\cdot (23x - 15)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-325)\pm\sqrt{(-325)^2-4(322)(75)}}{2(322)}=\frac{325\pm95}{644}\\&\text{Either way, we find thatthe function crosses the x-axis at} \ x=\frac{5}{14}\text{ and }\frac{15}{23}.\end{align*}$

Report an Error

Example Question #211 : College Algebra

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=140x^{2} - 548x - 168\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

x=-1176,80

$x=-\frac{2}{7},\frac{21}{5}$

x=1176,-80

$x=\frac{2}{7},-\frac{21}{5}$

Correct answer:

$x=-\frac{2}{7},\frac{21}{5}$

Explanation:

$\begin{align*}&\text{The function }f(x)=140x^{2} - 548x - 168\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&4\cdot (7x + 2)\cdot (5x - 21)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-548)\pm\sqrt{(-548)^2-4(140)(-168)}}{2(140)}=\frac{548\pm628}{280}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=-\frac{2}{7}\text{ and }\frac{21}{5}.\end{align*}$

Report an Error

Example Question #212 : College Algebra

$\begin{align*}&\text{Find the root(s) the function: }f(x)=270x^{2} - 596x - 448\end{align*}$

Possible Answers:

x=-1512,320

x=1512,-320

$x=\frac{14}{5},-\frac{16}{27}$

$x=-\frac{14}{5},\frac{16}{27}$

Correct answer:

$x=\frac{14}{5},-\frac{16}{27}$

Explanation:

$\begin{align*}&\text{The roots of the function }f(x)=270x^{2} - 596x - 448\text{ are the x values}\\&\text{that give it a value of zero. To find these x values}\\&\text{we can either factor the equation:}\\&2\cdot (27x + 16)\cdot (5x - 14)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-596)\pm\sqrt{(-596)^2-4(270)(-448)}}{2(270)}=\frac{596\pm916}{540}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{14}{5}\text{ and }-\frac{16}{27}.\end{align*}$

Report an Error

Example Question #213 : College Algebra

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=123x - 460x^{2} + 532\\&\text{has a zero value.}\end{align*}$

Possible Answers:

$x=-\frac{28}{23},\frac{19}{20}$

x=874,-1120

x=-874,1120

$x=\frac{28}{23},-\frac{19}{20}$

Correct answer:

$x=\frac{28}{23},-\frac{19}{20}$

Explanation:

$\begin{align*}&\text{Given }f(x)=123x - 460x^{2} + 532\text{, to find when it has a value of}\\&\text{zero, we need a method to determine the x values that}\\&\text{make this happen. We can either factor the equation:}\\&-(20x + 19)\cdot (23x - 28)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(123)\pm\sqrt{(123)^2-4(-460)(532)}}{2(-460)}=\frac{-123\pm997}{-920}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{28}{23}\text{ and }-\frac{19}{20}.\end{align*}$

Report an Error

Example Question #214 : College Algebra

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=100x^{2} - 627x - 324\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=\frac{27}{4},-\frac{12}{25}$

x=1350,-96

$x=-\frac{27}{4},\frac{12}{25}$

x=-1350,96

Correct answer:

$x=\frac{27}{4},-\frac{12}{25}$

Explanation:

$\begin{align*}&\text{The function }f(x)=100x^{2} - 627x - 324\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&(25x + 12)\cdot (4x - 27)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-627)\pm\sqrt{(-627)^2-4(100)(-324)}}{2(100)}=\frac{627\pm723}{200}\\&\text{Either way, we find thatthe function crosses the x-axis at} \ x=\frac{27}{4}\text{ and }-\frac{12}{25}.\end{align*}$

Report an Error

Example Question #215 : College Algebra

$\begin{align*}&\text{Find the root(s) the function: }f(x)=293x - 75x^{2} - 66\end{align*}$

Possible Answers:

x=-36,-550

$x=\frac{6}{25},\frac{11}{3}$

x=36,550

$x=-\frac{6}{25},-\frac{11}{3}$

Correct answer:

$x=\frac{6}{25},\frac{11}{3}$

Explanation:

$\begin{align*}&\text{The roots of the function }f(x)=293x - 75x^{2} - 66\text{ are the x values}\\&\text{that give it a value of zero. To find these x values}\\&\text{we can either factor the equation:}\\&-(25x - 6)\cdot (3x - 11)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(293)\pm\sqrt{(293)^2-4(-75)(-66)}}{2(-75)}=\frac{-293\pm257}{-150}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{6}{25}\text{ and }\frac{11}{3}.\end{align*}$

Report an Error

Example Question #216 : College Algebra

$\begin{align*}&\text{Find the root(s) the function: }f(x)=771x - 504x^{2} - 276\end{align*}$

Possible Answers:

$x=\frac{4}{7},\frac{23}{24}$

$x=-\frac{4}{7},-\frac{23}{24}$

x=576,966

x=-576,-966

Correct answer:

$x=\frac{4}{7},\frac{23}{24}$

Explanation:

$\begin{align*}&\text{The roots of the function }f(x)=771x - 504x^{2} - 276\text{ are the x values}\\&\text{that give it a value of zero. To find these x values}\\&\text{we can either factor the equation:}\\&-3\cdot (7x - 4)\cdot (24x - 23)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(771)\pm\sqrt{(771)^2-4(-504)(-276)}}{2(-504)}=\frac{-771\pm195}{-1008}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{4}{7}\text{ and }\frac{23}{24}.\end{align*}$

Report an Error

Example Question #217 : College Algebra

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=350x + 112x^{2} + 42\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=-3,-\frac{1}{8}$

$x=3,\frac{1}{8}$

x=-28,-672

x=28,672

Correct answer:

$x=-3,-\frac{1}{8}$

Explanation:

$\begin{align*}&\text{The function }f(x)=350x + 112x^{2} + 42\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&14\cdot (x + 3)\cdot (8x + 1)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(350)\pm\sqrt{(350)^2-4(112)(42)}}{2(112)}=\frac{-350\pm322}{224}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=-3\text{ and }-\frac{1}{8}.\end{align*}$

Report an Error

View College Algebra Tutors

Ger
Certified Tutor

Pennsylvania State University-Penn State Lehigh Valley, Bachelor of Science, Psychology.

View College Algebra Tutors

Daniel
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Psychology.

View College Algebra Tutors

Allyn
Certified Tutor

Indiana Wesleyan University, Master of Science, Business Administration and Management.

All College Algebra Resources

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

Popular Subjects

ISEE Tutors in San Diego, Computer Science Tutors in Seattle, ACT Tutors in Boston, English Tutors in Houston, Physics Tutors in Washington DC, LSAT Tutors in Atlanta, ACT Tutors in Atlanta, Physics Tutors in Seattle, Physics Tutors in Houston, LSAT Tutors in New York City

Popular Courses & Classes

SAT Courses & Classes in Atlanta, LSAT Courses & Classes in Seattle, SAT Courses & Classes in Phoenix, MCAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in New York City, GRE Courses & Classes in Seattle, GMAT Courses & Classes in Washington DC, Spanish Courses & Classes in Seattle, GRE Courses & Classes in Boston, SSAT Courses & Classes in Phoenix

Popular Test Prep

ACT Test Prep in Philadelphia, ISEE Test Prep in San Diego, SAT Test Prep in Atlanta, ISEE Test Prep in Atlanta, SSAT Test Prep in Washington DC, SSAT Test Prep in San Diego, GMAT Test Prep in Phoenix, MCAT Test Prep in Philadelphia, LSAT Test Prep in Atlanta, SSAT 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

College Algebra : Zeros/Roots of a Polynomial

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #31 : Polynomial Functions

Example Question #32 : Polynomial Functions

Example Question #32 : Polynomial Functions

Example Question #211 : College Algebra

Example Question #212 : College Algebra

Example Question #213 : College Algebra

Example Question #214 : College Algebra

Example Question #215 : College Algebra

Example Question #216 : College Algebra

Example Question #217 : College Algebra

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: