It is currently 20 Apr 2018, 15:20

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 29 Nov 2015
Posts: 11
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a [#permalink]

Show Tags

New post Updated on: 18 Jan 2016, 23:37
1
This post received
KUDOS
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (01:23) correct 33% (01:47) wrong based on 88 sessions

HideShow timer Statistics

If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a positive number t?

A. 2√15
B. 4√15
C. 3√13
D. 4√13
E. 6√15
[Reveal] Spoiler: OA

Originally posted by fattty on 18 Jan 2016, 23:32.
Last edited by Bunuel on 18 Jan 2016, 23:37, edited 1 time in total.
Edited the question.
Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8026
Location: Pune, India
Re: If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a [#permalink]

Show Tags

New post 18 Jan 2016, 23:58
2
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
fattty wrote:
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a positive number t?

A. 2√15
B. 4√15
C. 3√13
D. 4√13
E. 6√15



What is the meaning of this:
f(x), a quadratic in x, is tangent to x axis? It means that the graph of the quadratic touches x axis at only one point. So when y = 0, both roots are the same. So expression in x must be a perfect square when y = 0.

\(3x^2 - tx + 5 = 0\)

\((\sqrt{3}x)^2 - tx + (\sqrt{5})^2 = 0\)

To get a perfect square which looks like \(a^2 - 2ab + b^2 = (a - b)^2\), we must put \(tx = 2ab = 2*(\sqrt{3}x)*(\sqrt{5})\)

So t must be \(2*\sqrt{15}\)

Answer (A)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 5771
Re: If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a [#permalink]

Show Tags

New post 19 Jan 2016, 00:50
fattty wrote:
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a positive number t?

A. 2√15
B. 4√15
C. 3√13
D. 4√13
E. 6√15


Hi,
the equation is of a parabola..
and since its a tangent to x-axis, it means the parabola has min value as 0..
and where does this occur at x=-b/2a, so here, at x= t/6, or t=6x..
substitute the value of eq as 0..
f(x) = 3x^2 - tx + 5 ..
3x^2 - tx + 5 = 0..
3x^2 - 6x*x + 5 =0..
or x=\(\sqrt{\frac{5}{3}}\)...
so t=6x=6\(\sqrt{\frac{5}{3}}\)=2*\(\sqrt{15}\)
A
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


GMAT online Tutor

2 KUDOS received
Current Student
User avatar
Joined: 05 Apr 2014
Posts: 2
Location: India
Concentration: Technology, Operations
GMAT 1: 730 Q50 V38
GPA: 3.5
GMAT ToolKit User Premium Member
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a [#permalink]

Show Tags

New post 13 Mar 2016, 22:13
2
This post received
KUDOS
1
This post was
BOOKMARKED
fattty wrote:
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a positive number t?

A. 2√15
B. 4√15
C. 3√13
D. 4√13
E. 6√15



f(x) = \(3x^2 - tx + 5\), is a quadratic equation.
Given , X-axis is a tangent to this Quadratic equation , implies there is only one root for this equation .

As a result,the Discriminant (D) for this quadratic equation must be equal to 0.
We know that \(D=b^2-4*a*c\)
Ergo, since D=0

\(t^2-4*3*5=0\)
\(t^2=60\)
\(t=2\sqrt{15}\)


KUDOS if you liked the solution.
Kanishk


Attachments

File comment: Discriminant=0
Screen Shot 2016-03-14 at 10.43.19 AM.png
Screen Shot 2016-03-14 at 10.43.19 AM.png [ 63.41 KiB | Viewed 1435 times ]

BSchool Forum Moderator
User avatar
D
Joined: 12 Aug 2015
Posts: 2577
GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
Re: If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a [#permalink]

Show Tags

New post 15 Mar 2016, 01:23
fattty wrote:
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a positive number t?

A. 2√15
B. 4√15
C. 3√13
D. 4√13
E. 6√15




I am still confused about this Tangent to the axis thing...
How do you know that both the roots are the same..
chetan2u i did not understand your solution either..
can you Elaborate or provide the theory on the same..
_________________


Getting into HOLLYWOOD with an MBA

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

Average GRE Scores At The Top Business Schools!

Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 5771
Re: If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a [#permalink]

Show Tags

New post 15 Mar 2016, 06:16
Chiragjordan wrote:
fattty wrote:
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a positive number t?

A. 2√15
B. 4√15
C. 3√13
D. 4√13
E. 6√15




I am still confused about this Tangent to the axis thing...
How do you know that both the roots are the same..
chetan2u i did not understand your solution either..
can you Elaborate or provide the theory on the same..



Hi,

let me divide the Q in different sections..

A Linear Equation- a straight line
QUADRATIC equation:- the equation is of a parabola..
so if you have an equation like ax^2+bx+c=y.. and you plot the corresponding value of (x,y) on a graph
you will get a parabola- a U shaped or an inverted U shaped..
this has minimum value at the center of the Curve if it is U shaped and MAX value at the center of Curve if it is inverted U..

Now the equation or the curve is tangent to X-axis, meaning the curve just touches the X-axis at one point and thus this is the min value..
At X- axis y=0..
And the Curve is Symmetrical about a line determined by x=-b/2a..
so this will ofcourse meet the curve at the max/min value
----- we can derive this formula but not required here---

so the min value=0 at x=-b/2a
in equation f(x) = 3x^2 - tx + 5 .. b=-t and a=3
so x=-(-t)/2*3=t/6..
so t=6x..
and thereafter its all calculations..

f(x) = 3x^2 - tx + 5 ..
at x=t/6, y=0.. SO
3x^2 - tx + 5 = 0..
3x^2 - 6x*x + 5 =0..
or x=\(\sqrt{\frac{5}{3}}\)...
so t=6x=6\(\sqrt{\frac{5}{3}}\)=2*\(\sqrt{15}\)
A

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


GMAT online Tutor

1 KUDOS received
Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2652
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a [#permalink]

Show Tags

New post 23 Mar 2016, 12:16
1
This post received
KUDOS
fattty wrote:
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a positive number t?

A. 2√15
B. 4√15
C. 3√13
D. 4√13
E. 6√15


A more straightforward way is to realize that for a quadratic equation to be a perfect square ---> Discriminant = D = 0 ---> \(\sqrt{b^2-4*a*c} = 0\)

---> \(\sqrt{(-t)^2 -4*5*3} = 0\) ---> \(t^2 -4*5*3 = 0\) ---> \(t^2 = 60\) ---> \(t = 2 \sqrt{15}\)

P.S.: For any quadratic equation \(ax^2+bx+c = 0\)--->

1. 2 real unequal roots ---> D > 0
2. 2 equal roots (in the case of perfect squares) ---> D= 0
3. No real roots ---> D < 0
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 6641
Premium Member
Re: If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a [#permalink]

Show Tags

New post 14 Mar 2018, 05:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a   [#permalink] 14 Mar 2018, 05:35
Display posts from previous: Sort by

If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.