We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : How to find the solution to a quadratic equation

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #15 : How To Find The Solution To A Quadratic Equation

The expression $x^{2} - 8x +12$ is equal to 0 when $x = 2$ and $x = ?$

Possible Answers:

$6$

$-2$

$-6$

$-12$

$4$

Correct answer:

$6$

Explanation:

Factor the expression and set each factor equal to 0:

$(x-2)(x-6)= 0$

$x-2 = 0$

$x = 2$

$x-6 = 0$

$x = 6$

Report an Error

Example Question #21 : Quadratic Equations

Two positive consecutive multiples of four have a product of 96. What is the sum of the two numbers?

Possible Answers:

$20$

$8$

$12$

$24$

$16$

Correct answer:

$20$

Explanation:

Let $x$ = the first number and $x+4$ = the second number.

So the equation to solve becomes $x(x+4)=96$ . This quadratic equation needs to be multiplied out and set equal to zero before factoring. Then set each factor equal to zero and solve. Only positive numbers are correct, so the answer is $8+12=20$ .

Report an Error

Example Question #17 : How To Find The Solution To A Quadratic Equation

Two consecutive positive odd numbers have a product of 35. What is the sum of the two numbers?

Possible Answers:

Correct answer:

Explanation:

Let = first positive number and x+2 = second positive number.

The equation to solve becomes

x(x+2)=35

We multiply out this quadratic equation and set it equal to 0, then factor.

Report an Error

Example Question #18 : How To Find The Solution To A Quadratic Equation

The product of two consecutive positive multiples of four is 192. What is the sum of the two numbers?

Possible Answers:

Correct answer:

Explanation:

Let = the first positive number and x+4 = the second positive number

The equation to solve becomes x(x+4)=192

We solve this quadratic equation by multiplying it out and setting it equal to 0. The next step is to factor.

Report an Error

Example Question #22 : Quadratic Equations

Two consecutive positive multiples of three have a product of 504. What is the sum of the two numbers?

Possible Answers:

Correct answer:

Explanation:

Let = the first positive number and x + 3 = the second positive number.

So the equation to solve is x(x + 3) = 504

We multiply out the equation and set it equal to zero before factoring.

$x^{2} + 3x - 504 = 0$ thus the two numbers are 21 and 24 for a sum of 45.

Report an Error

Example Question #23 : Quadratic Equations

Two consecutive positive numbers have a product of 420. What is the sum of the two numbers?

Possible Answers:

Correct answer:

Explanation:

Let = first positive number and x + 1 = second positive number

So the equation to solve becomes x(x + 1) = 420

Using the distributive property, multiply out the equation and then set it equal to 0. Next factor to solve the quadratic.

Report an Error

Example Question #291 : Equations / Inequalities

A rectangle has a perimeter of $50\ m$ and an area of $150\ m^{2}$ What is the difference between the length and width?

Possible Answers:

$20\ m$

$25\ m$

$10\ m$

$5\ m$

$15\ m$

Correct answer:

$5\ m$

Explanation:

For a rectangle, $P=2w+2l$ and $A=lw$ where $w$ = width and $l$ = length.

So we get two equations with two unknowns:

$50=2w+2l$

$25=w+l$

$l=25-w$

$150=lw$

Making a substitution we get

$150=(25-w)w$

$w^{2} -25w + 150 = 0$

Solving the quadratic equation we get $w=10\ m$ or $15\ m$ .

$l=15\ m\ or\ 10\ m$

The difference is $5\ m$ .

Report an Error

Example Question #25 : Quadratic Equations

If $x(x^2-5x+3)=-9, \ x>0,\ and \ y^2+y=2$ then which of the following is a possible value for xy^2+y ?

Possible Answers:

Correct answer:

Explanation:

$x(x^2-5x+3)=-9, \ x>0,\ and \ y^2+y=2$

$x(x^2-5x+3)=-9 \Rightarrow x^3-5x^2+3x + 9=0\Rightarrow (x^2-6x+9)(x+1)$

$(x^2-6x+9)(x+1) = (x-3)^2(x+1)\Rightarrow x= -1\ or\ 3$

Since x>0 , x=3 .

$y^2+y-2=0 \Rightarrow (y+2)(y-1)=0 \Rightarrow y=-2\ or\ 1.$

Thus $xy^2+y = (3)(-2)^2+(-2)\ or\ (3)(1)^2+(1) = 12-2\ or\ 3+1\ = 10\ or\ 4$

Of these two, only 4 is a possible answer.

Report an Error

Example Question #21 : How To Find The Solution To A Quadratic Equation

Find all real solutions to the equation.

$x{^{2}+6x-16=0$

Possible Answers:

$-2\ \text{or}\ -8$

$2\ \text{or}\ -8$

$4\ \text{or}\ -4$

Correct answer:

$2\ \text{or}\ -8$

Explanation:

$x{^{2}+6x-16=0$

To solve by factoring, we need two numbers that add to $\small 6$ and multiply to $\small -16$ .

$-2*8=-16\ \text{and}\ -2+8=6$

(x-2)(x+8)=0

In order for the equation to equal zero, one of the terms must be equal to zero.

x-2=0

x=2

x+8=0

x=-8

Our final answer is that $x\epsilon\left \{ 2,-8 \right \}$ .

Report an Error

Example Question #22 : How To Find The Solution To A Quadratic Equation

How many real solutions are there for the following equation?

x^4 + 5x^2 - 14 = 0

Possible Answers:

Correct answer:

Explanation:

The first thing to notice is that you have powers with a regular sequence. This means you can simply treat it like a quadratic equation. You are then able to factor it as follows:

The factoring can quickly be done by noticing that the 14 must be either 7*2 or 14*1 . Because it is negative, one constant will be negative and the other positive. Finally, since the difference between 14 and 1 cannot be 5, it must be 7 and 2.

Alternatively, one could use the quadratic formula.

The end result is that you have:

$x^2 + 7 = 0\Rightarrow x^2 = -7 \ or \ x^2-2 = 0\Rightarrow x^2=2$

$x^2=2 \Rightarrow x=\pm \sqrt{2}$

$x^2=-7\Rightarrow x=\pm \sqrt-7$

The latter of these two gives only complex answers, so there are two real answers.

Report an Error

View PSAT Mathematics Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View PSAT Mathematics Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View PSAT Mathematics Tutors

Mohammad
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Mathematics. Rutgers University-New Brunswick, Master of Science, Stat...

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Philadelphia, Computer Science Tutors in Houston, Physics Tutors in Houston, ISEE Tutors in Denver, Calculus Tutors in Boston, Spanish Tutors in Philadelphia, Calculus Tutors in Washington DC, Physics Tutors in Philadelphia, SSAT Tutors in Denver, Calculus Tutors in Denver

Popular Courses & Classes

GMAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Washington DC, ACT Courses & Classes in Chicago, Spanish Courses & Classes in Denver, ACT Courses & Classes in Phoenix, MCAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Washington DC, GMAT Courses & Classes in San Diego, MCAT Courses & Classes in Chicago, MCAT Courses & Classes in Atlanta

Popular Test Prep

ISEE Test Prep in Miami, ACT Test Prep in Chicago, MCAT Test Prep in Boston, ISEE Test Prep in Washington DC, GRE Test Prep in Phoenix, GRE Test Prep in Dallas Fort Worth, MCAT Test Prep in Miami, ISEE Test Prep in San Diego, SAT Test Prep in Houston, ISEE 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

PSAT Math : How to find the solution to a quadratic equation

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #15 : How To Find The Solution To A Quadratic Equation

Example Question #21 : Quadratic Equations

Example Question #17 : How To Find The Solution To A Quadratic Equation

Example Question #18 : How To Find The Solution To A Quadratic Equation

Example Question #22 : Quadratic Equations

Example Question #23 : Quadratic Equations

Example Question #291 : Equations / Inequalities

Example Question #25 : Quadratic Equations

Example Question #21 : How To Find The Solution To A Quadratic Equation

Example Question #22 : How To Find The Solution To A Quadratic Equation

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: