We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : Finding Zeros 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 #3 : Solving Quadratic Functions

Find the roots of the function:
$\small f(x)=x^2+4x-12$

Possible Answers:

$\small x=-4\ or\ 3$

$\small \small x=-2\ or\ 6$

$\small \small x=2\ or\ -6$

$\small x=-3\ or\ 4$

Correct answer:

$\small \small x=2\ or\ -6$

Explanation:

Factor:

0=x^2+4x-12

$\small \small 0=(x-2)(x+6)$

Double check by factoring:

$\small F: (x)(x)$

$\small \small O:(x)(6)=6x$

$\small \small I: (-2)(x)=-2x$

$\small \small L: (-2)(6)=-12$

Add together: $\small x^2+6x-2x-12=x^2+4x-12$

Therefore:

$\small x-2=0\ or x+6=0$

$\small x=2\or-6$

Report an Error

Example Question #2 : Finding Zeros Of A Polynomial

Solve for x.

$x^{2}-7x+10=0$

Possible Answers:

x = 5, 2

x = –5, –2

x = 5

x = –4, –3

x = 4, 3

Correct answer:

x = 5, 2

Explanation:

1) Split up the middle term so that factoring by grouping is possible.

Factors of 10 include:

1 * 10= 10 1 + 10 = 11

2 * 5 =10 2 + 5 = 7

–2 * –5 = 10 –2 + –5 = –7 Good!

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

2) Now factor by grouping, pulling "x" out of the first pair and "-5" out of the second.

x(x-2)-5(x-2)=0

3) Now pull out the common factor, the "(x-2)," from both terms.

(x-5)(x-2)=0

4) Set both terms equal to zero to find the possible roots and solve using inverse operations.

x – 5 = 0, x = 5

x – 2 = 0, x = 2

Report an Error

Example Question #1 : How To Simplify Binomials

Solve for :

x^2+2 = 6x-6

Possible Answers:

x=1, 2

x=1,-2

x=-2,-4

x=2,4

Correct answer:

x=2,4

Explanation:

To solve for , you need to isolate it to one side of the equation. You can subtract the from the right to the left. Then you can add the 6 from the right to the left:

x^2+2 = 6x-6

x^2-6x+2 = -6

x^2-6x+8 = 0

Next, you can factor out this quadratic equation to solve for . You need to determine which factors of 8 add up to negative 6:

$(x \ \ \ \ \ \)(x \ \ \ \ \ \) = 0$

(x-2)(x-4)=0

Finally, you set each binomial equal to 0 and solve for :

$x=2 \ \ \ \ \ \ x=4$

Report an Error

Example Question #4 : Solving Quadratic Functions

Find the roots of the following quadratic expression:

6x^2 + 5x - 4

Possible Answers:

$x = \left \{ -\frac{1}{2}, \frac{4}{3}\right \}$

$x = \left \{ -4, 2\right \}$

$x = \left \{ -\frac{3}{4}, 2\right \}$

$x = \left \{ -\frac{4}{3}, \frac{1}{2}\right \}$

$x = \left \{ -1, 4\}$

Correct answer:

$x = \left \{ -\frac{4}{3}, \frac{1}{2}\right \}$

Explanation:

First, we have to know that "finding the roots" means "finding the values of x which make the expression =0." So basically we are going to set the original expression = 0 and factor.

6x^2 + 5x - 4 = 0

This quadratic looks messy to factor by sight, so we'll use factoring by composition. We multiply a and c together, and look for factors that add to b.

6 * -4 = -24

-24 = 8 * -3

8 + -3 = 5

So we can use 8 and -3. We will re-write 5x using these numbers as 8x - 3x, and then factor by grouping.

6x^2 + 5x - 4 = 0

6x^2 + 8x - 3x - 4 = 0

(6x^2 + 8x) + (- 3x - 4) = 0

Note the extra + sign we inserted to make sure the meaning is not lost when parentheses are added. Now we identify common factors to be "pulled" out.

(3x(2x) + 4(2x)) + ((-1) 3x +(-1) 4) = 0

2x(3x+4)) + -1( 3x + 4) = 0

Now we factor out the (3x + 4).

(3x+4)(2x-1)=0

Setting each factor = 0 we can find the solutions.

2x - 1 =0

2x = 1

x = 1/2

3x + 4 = 0

3x = -4

$x = \frac{-4}{3}$

So the solutions are x = 1/2 and x = -4/3, or {-4/3, 1/2}.

Report an Error

Example Question #1 : Finding Zeros Of A Polynomial

Find the roots of $\small 9x^2 -121$ .

Possible Answers:

$\small x=\pm\frac{11}{9}$

$\small x=\pm\frac{3}{11}$

$\small x=\pm\frac{11}{3}$

$\small x=\pm11$

$\small x=0$

Correct answer:

$\small x=\pm\frac{11}{3}$

Explanation:

If we recognize this as an expression with form $\small a^2 - b^2$ , with $\small a=3x$ and $\small b=121$ , we can solve this equation by factoring:

$\small 9x^2-121=0$

$\small (3x+11)(3x-11)=0$

$\small 3x+11=0$ and $\small 3x-11=0$

$\small x=-\frac{11}{3}$ and $\small x=\frac{11}{3}$

Report an Error

Example Question #2 : Finding Zeros Of A Polynomial

If the following is a zero of a polynomial, find another zero.

3+i

Possible Answers:

3+i

i-3

unknown

3-i

Correct answer:

3-i

Explanation:

When finding zeros of a polynomial, you must remember your rules. Without a function this may seem tricky, but remember that non-real solutions come in conjugate pairs. Conjugate pairs differ in the middle sign. Thus, our answer is:

3-i

Report an Error

Example Question #1 : Finding Zeros Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=200x - 320x^{2} + 250\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

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

$x=-\frac{3215}{16},-\frac{3185}{16}$

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

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

Correct answer:

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

Explanation:

$\begin{align*}&\text{The function }f(x)=200x - 320x^{2} + 250\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&-10\cdot (8x + 5)\cdot (4x - 5)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(200)\pm\sqrt{(200)^2-4(-320)(250)}}{2(-320)}=\frac{-200\pm600}{-640}\\&\text{Either way, we find thatthe function crosses the x-axis at} x=\frac{5}{4}\text{ and }-\frac{5}{8}.\end{align*}$

Report an Error

Example Question #2 : Finding Zeros Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=732x - 96x^{2} - 702\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=-\frac{11755}{16},-\frac{11669}{16}$

$x=-\frac{13}{2},-\frac{9}{8}$

$x=26,\frac{9}{2}$

$x=\frac{13}{2},\frac{9}{8}$

Correct answer:

$x=\frac{13}{2},\frac{9}{8}$

Explanation:

$\begin{align*}&\text{The function }f(x)=732x - 96x^{2} - 702\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&-6\cdot (8x - 9)\cdot (2x - 13)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(732)\pm\sqrt{(732)^2-4(-96)(-702)}}{2(-96)}=\frac{-732\pm516}{-192}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{13}{2}\text{ and }\frac{9}{8}.\end{align*}$

Report an Error

Example Question #3 : Finding Zeros Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=38x + 208x^{2} - 126\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=\frac{7}{8},-\frac{9}{13}$

$x=-\frac{7}{2},\frac{36}{13}$

$x=-\frac{7741}{208},-\frac{8067}{208}$

$x=-\frac{7}{8},\frac{9}{13}$

Correct answer:

$x=-\frac{7}{8},\frac{9}{13}$

Explanation:

$\begin{align*}&\text{The function }f(x)=38x + 208x^{2} - 126\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&2\cdot (8x + 7)\cdot (13x - 9)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(38)\pm\sqrt{(38)^2-4(208)(-126)}}{2(208)}=\frac{-38\pm326}{416}\\&\text{Either way, we find thatthe function crosses the x-axis at} \ x=-\frac{7}{8}\text{ and }\frac{9}{13}.\end{align*}$

Report an Error

Example Question #9 : Finding Zeros Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=524x + 272x^{2} + 84\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=-7,-\frac{12}{17}$

$x=\frac{7}{4},\frac{3}{17}$

$x=-\frac{71157}{136},-\frac{71371}{136}$

$x=-\frac{7}{4},-\frac{3}{17}$

Correct answer:

$x=-\frac{7}{4},-\frac{3}{17}$

Explanation:

$\begin{align*}&\text{The function }f(x)=524x + 272x^{2} + 84\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&4\cdot (4x + 7)\cdot (17x + 3)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(524)\pm\sqrt{(524)^2-4(272)(84)}}{2(272)}=\frac{-524\pm428}{544}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=-\frac{7}{4}\text{ and }-\frac{3}{17}.\end{align*}$

Report an Error

View College Algebra Tutors

Priyanka
Certified Tutor

CUNY Hunter College, Bachelor in Arts, Economics.

View College Algebra Tutors

Vince
Certified Tutor

Salt Lake Community College, Associate in Science, Mathematics.

View College Algebra Tutors

Shifrah
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Biology, General. Massachusetts College of Pharmacy and Health ...

All College Algebra Resources

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

Popular Subjects

Math Tutors in San Francisco-Bay Area, Chemistry Tutors in Phoenix, Computer Science Tutors in Denver, SSAT Tutors in Washington DC, MCAT Tutors in Philadelphia, Biology Tutors in New York City, Spanish Tutors in Chicago, SAT Tutors in Los Angeles, Statistics Tutors in Chicago, SSAT Tutors in San Francisco-Bay Area

Popular Courses & Classes

SAT Courses & Classes in Chicago, GRE Courses & Classes in Philadelphia, GMAT Courses & Classes in Los Angeles, SAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Chicago, ISEE Courses & Classes in Houston, GRE Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Denver, GRE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ISEE Test Prep in Dallas Fort Worth, SSAT Test Prep in New York City, GMAT Test Prep in Philadelphia, GMAT Test Prep in Boston, GRE Test Prep in Atlanta, MCAT Test Prep in Denver, ISEE Test Prep in Chicago, GRE Test Prep in Philadelphia, LSAT Test Prep in Denver, GRE Test Prep in San Francisco-Bay Area

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 : Finding Zeros of a Polynomial

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #3 : Solving Quadratic Functions

Example Question #2 : Finding Zeros Of A Polynomial

Example Question #1 : How To Simplify Binomials

Example Question #4 : Solving Quadratic Functions

Example Question #1 : Finding Zeros Of A Polynomial

Example Question #2 : Finding Zeros Of A Polynomial

Example Question #1 : Finding Zeros Of A Polynomial

Example Question #2 : Finding Zeros Of A Polynomial

Example Question #3 : Finding Zeros Of A Polynomial

Example Question #9 : Finding Zeros 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: