Last visit was: 21 May 2024, 18:49 It is currently 21 May 2024, 18:49
Toolkit
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

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.

# If f(x^2) = x^4 6x^2 + 5, which of the following must be true?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625650 [8]
Given Kudos: 81918
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1779
Own Kudos [?]: 2106 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3138
Own Kudos [?]: 4449 [3]
Given Kudos: 1856
Location: India
Director
Joined: 29 Oct 2015
Posts: 730
Own Kudos [?]: 333 [0]
Given Kudos: 477
Re: If f(x^2) = x^4 6x^2 + 5, which of the following must be true? [#permalink]
KarishmaB can you provide a quick and easy solution to this question please ?

Posted from my mobile device
Director
Joined: 16 Jul 2019
Posts: 540
Own Kudos [?]: 208 [0]
Given Kudos: 150
Re: If f(x^2) = x^4 6x^2 + 5, which of the following must be true? [#permalink]
sayan640 wrote:
KarishmaB can you provide a quick and easy solution to this question please ?

Posted from my mobile device

The biquadratic function is symmetric in some line x^2=(5+1)/2=3
f(3+t)=f(3-t)

f(0)=f(6)=5.
Director
Joined: 29 Oct 2015
Posts: 730
Own Kudos [?]: 333 [0]
Given Kudos: 477
Re: If f(x^2) = x^4 6x^2 + 5, which of the following must be true? [#permalink]
Oppenheimer1945 wrote:
sayan640 wrote:
KarishmaB can you provide a quick and easy solution to this question please ?

Posted from my mobile device

The biquadratic function is symmetric in some line x^2=(5+1)/2=3
f(3+t)=f(3-t)

f(0)=f(6)=5.
Director
Joined: 16 Jul 2019
Posts: 540
Own Kudos [?]: 208 [0]
Given Kudos: 150
If f(x^2) = x^4 6x^2 + 5, which of the following must be true? [#permalink]
sayan640 wrote:
Oppenheimer1945 wrote:
sayan640 wrote:
KarishmaB can you provide a quick and easy solution to this question please ?

Posted from my mobile device

The biquadratic function is symmetric in some line x^2=(5+1)/2=3
f(3+t)=f(3-t)

f(0)=f(6)=5.

­Pls understand that the quadratic is symmertical. Let's say $$f(x)=x^2$$, the function is symmetrical about y-axis or $$x=0.$$
Hence we can say $$f(k)=f(-k)$$,... the even function property.

here  $$x=0$$ is the point of extrema.

Same concept can be applied here after converting the bi-quadratic into a quadratic by basic substituon of $$x^2=t$$.

the point of minima is the average of roots. Hence, function is symmertical about the line x= avg of root (1,5)=3.

Hence $$f(3+t)=f(3-t)­$$­ and option E follows
If f(x^2) = x^4 6x^2 + 5, which of the following must be true? [#permalink]
Moderator:
Math Expert
93373 posts