BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

What is the sum of all values of that satisfy the equation

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Sat May 04, 2019 11:40 am
We can divide by 4 and get zero on both sides:

4x^2 + 16 = 32x
x^2 + 4 = 8x
x^2 - 8x + 4 = 0

When we factor the left side above, the factorization will look like (x - a)(x - b), where a and b are the two solutions to the quadratic. The numbers a and b will multiply to 4 (since 4 = (-a)(-b) = ab) and will add to 8 (since -a and -b will add to -8), and since a and b are the solutions to the quadratic, a+b = 8 is the answer.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
User avatar
GMAT Instructor
Posts: 8132
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Mon May 13, 2019 5:39 pm
BTGmoderatorLU wrote:Source: Veritas Prep

What is the sum of all values of that satisfy the equation \(4x^2 +16=32x\)?

A. \(−8\)
B. \(−4\sqrt{2}\)
C. \(−4\)
D. \(4\sqrt{2}\)
E. \(8\)

The OA is E
Setting the equation to 0, we have:

4x^2 - 32x + 16 = 0

For a quadratic equation of the form ax^2 + bx + c = 0 (where a ≠ 0), the sum of the roots (or solutions) is always -b/a. Therefore, the sum of the roots in this case is -(-32)/4 = 32/4 = 8.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1