Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Solve a Quadratic Equation

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Solve A Quadratic Equation

Solve the following quadratic equation:

3x^2-9x-84=0

Possible Answers:

$x=\frac{3}{2},x=4$

x=-4,x=7

x=1,x=3

x=-6,x=8

x=-2,x=5

Correct answer:

x=-4,x=7

Explanation:

When solving a quadratic equation, the first thing to look for is whether or not it can be factored, as this is most often the easiest and fastest method if the quadratic can in fact be factored. We can see that each of the terms in the given equation have a common factor of 3, so it will be easier to factor the quadratic if we first factor out the 3:

3x^2-9x-84=0

3(x^2-3x-28)=0

Now we're left with a polynomial where we need to find two numbers whose product is -28 and whose sum is -3. Thinking about the factors of 28, we can see that 4 and 7 will yield -3 if 7 is negative and 4 is positive, so we now have our factorization:

3(x-7)(x+4)=0

$x-7=0\rightarrow x=7$

$x+4=0\rightarrow x=-4$

Report an Error

Example Question #1 : Solve A Quadratic Equation

Find the root(s) of the following quadratic equation?

y=x^2+9x+20

Possible Answers:

x={4,5}

x={-10,-2}

x=3

x={2,10}

x={-5,-4}

Correct answer:

x={-5,-4}

Explanation:

To find the roots of an equation in the form y=ax^2+bx+c , you use the quadratic formula

$\frac{(-b\pm\sqrt{b^2-4ac})}{(2a)}$ .

In our case, we have a=1, b=9, c=20 .

This gives us $\frac{(-9\pm\sqrt{9^2-4(1)(20)})}{2}$ which simplifies to

$\frac{(-9\pm\sqrt{81-80})}{2}=\frac{(-9\pm1)}{2}={-5,-4}$

Report an Error

Example Question #2 : Solve A Quadratic Equation

Given the function y=x^2-20x+51 , find a possible root for this quadratic.

Possible Answers:

Correct answer:

Explanation:

Factorize y=x^2-20x+51 and set this equation equal to zero.

y=x^2-20x+51=(x-17)(x-3)

(x-17)(x-3)=0

x=17,3

The answer is one of the possible choices.

Report an Error

Example Question #3 : Solve A Quadratic Equation

Solve the quadratic equation for .

(x-4)^2-16=0

Possible Answers:

None of the other answers.

Correct answer:

None of the other answers.

Explanation:

There are two solutions; x=0, x=8 .

We proceed as follows.

(x-4)^2-16=0

Add to both sides.

(x-4)^2=16

Take the square root of both sides, remember to introduce plus/minus on the right side since you are introducing a square root into your work.

$x-4 = \pm4$

Add to both sides.

x = 0, 8

Report an Error

Example Question #1 : Solve A Quadratic Equation

Solve the quadratic equation for .

4x^2 +5x -6 = 0

Use the quadratic formula.

Possible Answers:

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

None of the other answers.

4,0

$-\frac{5}{8} \pm \frac{1}{8}\sqrt{71}i$

Correct answer:

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

Explanation:

For any quadtratic equation of the form ax^2+bx+c=0 , the quadratic formula is

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

Plugging in our given values a = 4, b=5, c=-6 we have:

$x = \frac{-5 \pm \sqrt{25+96}}{8}$

$x = -\frac{5}{8} \pm \frac{\sqrt{121}}{8}$

$x= -\frac{5}{8} \pm \frac{11}{8}$

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

Report an Error

Example Question #6 : Solve A Quadratic Equation

Find the roots of the equation.

$2x^{2}-x-6=0$

Possible Answers:

$x=\pm3$

$x=2,\: \:x=-\frac{3}{2}$

$x=3,\: \:x=-\frac{5}{3}$

$x=7,\: \:x=3$

$x=2,\: \:x=-7$

Correct answer:

$x=2,\: \:x=-\frac{3}{2}$

Explanation:

Use either the quadratic formula or factoring to solve the quadratic equation.

Using factoring, we want to find which factors of six when multiplied with the factors of two and then added together result in negative one.

$2x^{2}-x-6=0$

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

$x=2,\: \:x=-\frac{3}{2}$

Using the quadratic formula,

let

a=2, b=-1, c=-6

$x=\frac{1\pm\sqrt{1-4(2)(-6)}}{2(2)}$

$x=\frac{1\pm \sqrt{1+48}}{4}$

$\\x=\frac{1\pm \sqrt{49}}{4}=\frac{1\pm7}{4}\\ \\x=2, -\frac{3}{2}$

Report an Error

Example Question #7 : Solve A Quadratic Equation

Solve f(x)=3x^2-4x+1 .

Possible Answers:

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

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

$x=0, \frac{1}{3}$

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

Correct answer:

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

Explanation:

To solve this equation, use trial and error to factor it. Since the leading coefficient is , there is only one way to get $(3\cdot1)$ , so that is helpful reminder. Once it's properly factored, you get: (3x-1)(x-1) . Then, set both of those expressions equal to to get your roots: $x=1, \frac{1}{3}$ .

Report an Error

View Pre-Calculus Tutors

James
Certified Tutor

St. Mary of the Plains College, Bachelors, Mathematics. Baker University, Masters, Business Administration and Management.

View Pre-Calculus Tutors

Satweka
Certified Tutor

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

View Pre-Calculus Tutors

Pankaj
Certified Tutor

University of Delhi, Electrical Engineer, Electrical Engineering. Columbia University in the City of New York, Master of Arts...

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in San Francisco-Bay Area, Statistics Tutors in Washington DC, GRE Tutors in Dallas Fort Worth, Biology Tutors in Boston, Calculus Tutors in Houston, Statistics Tutors in Boston, Statistics Tutors in Atlanta, English Tutors in Seattle, GRE Tutors in Washington DC, Computer Science Tutors in Houston

Popular Courses & Classes

SSAT Courses & Classes in New York City, GMAT Courses & Classes in Denver, SSAT Courses & Classes in Washington DC, SAT Courses & Classes in Los Angeles, SAT Courses & Classes in Houston, MCAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Philadelphia, LSAT Courses & Classes in San Diego, Spanish Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

MCAT Test Prep in New York City, GRE Test Prep in New York City, LSAT Test Prep in San Diego, MCAT Test Prep in Chicago, SAT Test Prep in Denver, GRE Test Prep in Dallas Fort Worth, LSAT Test Prep in Seattle, SSAT Test Prep in San Diego, ISEE Test Prep in Philadelphia, ACT 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

Precalculus : Solve a Quadratic Equation

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Solve A Quadratic Equation

Example Question #1 : Solve A Quadratic Equation

Example Question #2 : Solve A Quadratic Equation

Example Question #3 : Solve A Quadratic Equation

Example Question #1 : Solve A Quadratic Equation

Example Question #6 : Solve A Quadratic Equation

Example Question #7 : Solve A Quadratic Equation

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: