Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
15 Jun 2022, 01:31
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
41% (03:14) correct
59%
(03:24)
wrong
based on 85
sessions
History
Date
Time
Result
Not Attempted Yet
If one of the roots of the equation \(2x^2 + (3k + 4)x + (9k^2 – 3k – 1) = 0\) is twice the other, then which of the following can be a value of ‘k’?
A. \(\frac{-2}{3}\)
B. \(\frac{2}{3}\)
C. \(\frac{-1}{3}\)
D. \(\frac{1}{3}\)
E. None of the above
Are You Up For the Challenge: 700 Level Questions
A. \(\frac{-2}{3}\)
B. \(\frac{2}{3}\)
C. \(\frac{-1}{3}\)
D. \(\frac{1}{3}\)
E. None of the above
Are You Up For the Challenge: 700 Level Questions
15 Jun 2022, 05:41
Kudos
Bookmarks
If one of the roots of the equation 2x2+(3k+4)x+(9k2–3k–1)=0 is twice the other, then which of the following can be a value of ‘k’?
Let the roots of a quadratic equation be p and q.
Since for a standard quadratic equation a\(x^2\)+bx+c=0,
Sum of roots, p+q=\(\frac{-b}{a}\)
Product of roots,pq=\(\frac{c}{a}\)
Now , in this equation 2\(x^2\)+(3k+4)x+(9\(k^2\)-3k-1)=0
If we compare it with standard quadratic equation we get,
a=2,b=3k+4,c=9\(k^2\)-3k-1
Also it is given, one root is twice of the other
so let roots of this equation be p and 2p
Sum of roots, p+2p=\(\frac{-(3k+4)}{2}\) ............(1)
Product of root, p*2p=\(\frac{9k^2-3k-1}{2}\) ............(2)
Solving equation (1)
p+2p=\(\frac{-(3k+4)}{2}\)
3p=\(\frac{-(3k+4)}{2}\)
p=\(\frac{-(3k+4)}{6}\)
Squaring both sides
\(p^2\)=\(\frac{(3k+4)^2}{36}\)
\(p^2\)=\(\frac{9k^2+16+24k}{36 }\) ...........(3)
Now, solving equation (2)
\(p*2p\) =\(\frac{9k^2-3k-1}{2}\)
\(2p^2\) =\(\frac{9k^2-3k-1}{2 } \)
\(p^2\) =\(\frac{9k^2-3k-1}{4 } \) ...........(4)
Equating value of \(p^2\) from equation(3) and equation(4)
\(\frac{9k^2+16+24k}{36}\) = \(\frac{9k^2-3k-1}{4}\)
\(\frac{9k^2+16+24k}{9}\) = \(9k^2-3k-1\)
\(9k^2+16+24k\) = \(81k^2-27k-9\)
\(72k^2-51k-25\) =0
\(72k^2-75k+24k-25\) =0
3k (24k - 25)+1(24k - 25) =0
(3k + 1) (24k - 25) =0
k= \(\frac{-1}{3}\) and k=\(\frac{25}{24}\)
Among the options given, k=\(\frac{-1}{3}\)
Hence, C
Let the roots of a quadratic equation be p and q.
Since for a standard quadratic equation a\(x^2\)+bx+c=0,
Sum of roots, p+q=\(\frac{-b}{a}\)
Product of roots,pq=\(\frac{c}{a}\)
Now , in this equation 2\(x^2\)+(3k+4)x+(9\(k^2\)-3k-1)=0
If we compare it with standard quadratic equation we get,
a=2,b=3k+4,c=9\(k^2\)-3k-1
Also it is given, one root is twice of the other
so let roots of this equation be p and 2p
Sum of roots, p+2p=\(\frac{-(3k+4)}{2}\) ............(1)
Product of root, p*2p=\(\frac{9k^2-3k-1}{2}\) ............(2)
Solving equation (1)
p+2p=\(\frac{-(3k+4)}{2}\)
3p=\(\frac{-(3k+4)}{2}\)
p=\(\frac{-(3k+4)}{6}\)
Squaring both sides
\(p^2\)=\(\frac{(3k+4)^2}{36}\)
\(p^2\)=\(\frac{9k^2+16+24k}{36 }\) ...........(3)
Now, solving equation (2)
\(p*2p\) =\(\frac{9k^2-3k-1}{2}\)
\(2p^2\) =\(\frac{9k^2-3k-1}{2 } \)
\(p^2\) =\(\frac{9k^2-3k-1}{4 } \) ...........(4)
Equating value of \(p^2\) from equation(3) and equation(4)
\(\frac{9k^2+16+24k}{36}\) = \(\frac{9k^2-3k-1}{4}\)
\(\frac{9k^2+16+24k}{9}\) = \(9k^2-3k-1\)
\(9k^2+16+24k\) = \(81k^2-27k-9\)
\(72k^2-51k-25\) =0
\(72k^2-75k+24k-25\) =0
3k (24k - 25)+1(24k - 25) =0
(3k + 1) (24k - 25) =0
k= \(\frac{-1}{3}\) and k=\(\frac{25}{24}\)
Among the options given, k=\(\frac{-1}{3}\)
Hence, C
15 Jun 2022, 06:04
Kudos
Bookmarks
varunrai1992
Any hint in solving
\(72k^2-51k-25\) =0
with such a clever way?
I may likely give up at this very moment.
