Last visit was: 26 Jul 2024, 17:25 It is currently 26 Jul 2024, 17:25
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the minimum possible value of x^2 – 6x + 14?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 94619
Own Kudos [?]: 644161 [21]
Given Kudos: 86770
Send PM
CAT Tests Forum Quiz Mode
What is the minimum possible value of x^2 – 6x + 14? [#permalink] What is the minimum possible value of x^2 – 6x + 14?   20 May 2020, 08:02
2
Kudos
18
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

70% (01:20) correct 30% (01:37) wrong based on 290 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
What is the minimum possible value of \(x^2 – 6x + 14\)?

A. 0
B. 1
C. 5
D. 6
E. 14
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
Own Kudos [?]: 9470 [7]
Given Kudos: 91
 Q51  V47
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink] What is the minimum possible value of x^2 – 6x + 14?   29 Jun 2020, 03:08
6
Kudos
1
Bookmarks
Expert Reply
Bunuel wrote:
What is the minimum possible value of \(x^2 – 6x + 14\)?

A. 0
B. 1
C. 5
D. 6
E. 14


The standard way to solve questions like this (without formulas you'd never need on the GMAT) is by "completing the square". If we first look only at this part of the quadratic:

x^2 - 6x

we can make this into a perfect square by adding 9:

x^2 - 6x + 9 = (x - 3)^2

We see how to do that just by dividing the "-6" by 2. So using that in the original question:

x^2 - 6x + 14 = x^2 - 6x + 9 + 5 = (x - 3)^2 + 5

and since (x-3)^2 is a square, its minimum value is 0 (when x = 3), so the minimum value of (x - 3)^2 + 5 is equal to 5.

I can't recall a single official question where I've needed to use this technique, though.
General Discussion
avatar
B
rimco2552
Intern
Intern
Joined: 29 Apr 2020
Posts: 17
Own Kudos [?]: 12 [2]
Given Kudos: 19
WE:Analyst (Computer Software)
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink] What is the minimum possible value of x^2 – 6x + 14?   20 May 2020, 08:30
2
Kudos
This can be solved by a simple formula:

Max or minimum value of a quadratic equation "ax^2+bx+c" is given by:

max/min = c- (b^2/4a)

Now, if the Coefficient of x^2 (a) is positive, the equation will have a minimum value where else it the same is negative, it will have a maximum value.

Hence, the minimum value of the given eq is:

14 - (36/4) = 14-9 = 5 (Answer : C)
User avatar
G
rishab0507
Manager
Manager
Joined: 12 Mar 2019
Posts: 182
Own Kudos [?]: 105 [0]
Given Kudos: 105
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink] What is the minimum possible value of x^2 – 6x + 14?   20 Jun 2020, 06:49
For a quadratic function of the form ax^2 + bx + c where a>0, the minimum value of the function is given by 4ac–b^2/4a

Putting values:
4*1*14 - (6)^2 /4*1 = 20/4 = > 5

Answer C
avatar
B
vaibhav101
Intern
Intern
Joined: 21 Apr 2017
Posts: 36
Own Kudos [?]: 23 [0]
Given Kudos: 256
GMAT 1: 560 Q43 V24
GMAT 2: 580 Q44 V25
GMAT 3: 540 Q44 V20
Send PM
What is the minimum possible value of x^2 – 6x + 14? [#permalink] What is the minimum possible value of x^2 – 6x + 14?   20 Jun 2020, 11:57
Bunuel wrote:
What is the minimum possible value of \(x^2 – 6x + 14\)?

A. 0
B. 1
C. 5
D. 6
E. 14


No formula approach.

\(x^2 – 6x + 14\) = \(x^2 – 6x + 8 + 6\) = \(x^2 – 2x - 4x + 8 + 6\) = (x-2) (x-4) + 6

Remember here, \(x\geq{2}\). Now at x = 2,4 the the value will be 6 , but at x=3, the minimum value will be 5.

So Answer is C.
User avatar
B
RajDev95
Intern
Intern
Joined: 21 Feb 2019
Posts: 3
Own Kudos [?]: 1 [0]
Given Kudos: 32
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink] What is the minimum possible value of x^2 – 6x + 14?   29 Jun 2020, 00:09
Think of it as 10+x^2.
For us to get the minimum value, we can only assign x to 0 (x=0).
Since there is no point in assigning a negative number because of the square.
Now let's work on the question.

x^2–6x+14
x^2-6x+9+5
(x^2-2.x.3+3^2)+5
(x-3)^2+5

So, the minimum value here is 5.

ANS is C.
User avatar
B
Satishqwerty
Intern
Intern
Joined: 12 Oct 2019
Posts: 47
Own Kudos [?]: 39 [0]
Given Kudos: 8
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink] What is the minimum possible value of x^2 – 6x + 14?   29 Jun 2020, 05:47
The minimum value of a quadratic equation occurs at \(\frac{-b}{2a}\)

The minimum value will occur at \(\frac{-(-6)}{2 \times 1} = 3\)

Putting the value \(x = 3\) in the equation \(x^2 – 6x + 14\)

\(3^2 - 6 \times 3 + 14 = 9 + 14 - 18 = 23 - 18 = 5\)

OA, C
Bunuel wrote:
What is the minimum possible value of \(x^2 – 6x + 14\)?

A. 0
B. 1
C. 5
D. 6
E. 14
User avatar
L
mSKR
VP
VP
Joined: 14 Aug 2019
Posts: 1346
Own Kudos [?]: 857 [1]
Given Kudos: 381
Location: Hong Kong
Concentration: Strategy, Marketing
Schools: IE (A) IIML-IPMX '22 (A) HKUST '22
GMAT 1: 650 Q49 V29
GPA: 3.81
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink] What is the minimum possible value of x^2 – 6x + 14?   29 Jun 2020, 05:55
1
Kudos
b^2-4ac>= 0 ( because factor of x can be found by x = -b+(or-)sqrt ( b^2-4ac)/2a
i can only change value of c to find the minimum value of expression ( x^2–6x+14 )
36-4c>0 --> c=<9 ==> c= 9 for expression to have 0
current value of c is 14
so minimum value of given expression is 14-9 = 5 ( it would be (x-some factor)^2+ 5= 0
User avatar
B
BlueRocketAsh
Manager
Manager
Joined: 11 Oct 2019
Posts: 76
Own Kudos [?]: 11 [0]
Given Kudos: 2
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink] What is the minimum possible value of x^2 – 6x + 14?   30 Jun 2020, 15:33
x^2–6x+14
= x^2-6x+9+5
= (x-3)^2+5
Minimum value of square term is 0
Therefore minimum value of the expression is 5
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 34108
Own Kudos [?]: 854 [0]
Given Kudos: 0
Send PM
Re: What is the minimum possible value of x^2 6x + 14? [#permalink] What is the minimum possible value of x^2 – 6x + 14?   27 Mar 2024, 08:05
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 Club Bot
gmatclubot
Re: What is the minimum possible value of x^2 6x + 14? [#permalink]
27 Mar 2024, 08:05
Moderator:
Bunuel
Math Expert
94619 posts