If there is exactly one solution to the equation \(25x^2-bx+64=0\), where \(b>0\), what is the value of \(b\)?
A. 26
B. 40
C. 52
D. 80
E. 100
The OA is D
Source: Veritas Prep
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
If there is exactly one solution to the equation \(25x^2\)
This topic has expert replies
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Since the quadratic equation has only one solution, it means the left hand side of the equation must be a perfect square. Therefore, we can factor the left hand side as:swerve wrote:If there is exactly one solution to the equation \(25x^2-bx+64=0\), where \(b>0\), what is the value of \(b\)?
A. 26
B. 40
C. 52
D. 80
E. 100
The OA is D
Source: Veritas Prep
(5x + 8)^2 or (5x - 8)^2
Expanding the first perfect square, we have: (5x + 8)^2 = 25x^2 + 80x + 64, so -b = 80 or b = -80. However, b is positive. So b can't be -80. Let's expand the second perfect square:
(5x - 8)^2 = 25x^2 - 80x + 64
-b = -80
b = 80
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
