It is currently 18 Mar 2018, 14:36

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the equation x^2+kx+1=0, x is a variable and k is a constant

Author Message
TAGS:

### Hide Tags

Manager
Joined: 08 May 2015
Posts: 101
GMAT 1: 630 Q39 V38
GMAT 2: 670 Q44 V38
GMAT 3: 750 Q49 V44
In the equation x^2+kx+1=0, x is a variable and k is a constant [#permalink]

### Show Tags

10 Aug 2015, 17:53
11
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:15) correct 43% (01:19) wrong based on 168 sessions

### HideShow timer Statistics

In the equation $$x^2+kx+1=0$$, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true?

I) k=0

II) k=−1

III) k=−3

A) I only
B) III only
C) I and II only
D) II and III only
E) I and III only
[Reveal] Spoiler: OA

Last edited by ENGRTOMBA2018 on 10 Aug 2015, 18:03, edited 1 time in total.
Formatted the question
Current Student
Joined: 20 Mar 2014
Posts: 2685
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: In the equation x^2+kx+1=0, x is a variable and k is a constant [#permalink]

### Show Tags

10 Aug 2015, 18:05
2
KUDOS
2
This post was
BOOKMARKED
Mascarfi wrote:
In the equation $$x^2+kx+1=0$$, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true?

I) k=0

II) k=−1

III) k=−3

A) I only
B) III only
C) I and II only
D) II and III only
E) I and III only

Per the question, $$x^2+kx+1=0$$ with k=constant.

For a quadratic equation ($$ax^2+bx+c=0$$) to have 2 distinct roots ---> $$D =b^2-4ac > 0$$ ---> $$k^2-4>0$$ --->$$k<-2$$or $$k>2$$ . Only III falls in these ranges. B is the correct answer.
Intern
Joined: 22 Jun 2016
Posts: 47
Re: In the equation x^2+kx+1=0, x is a variable and k is a constant [#permalink]

### Show Tags

14 Oct 2016, 20:08
Engr2012 wrote:
Mascarfi wrote:
In the equation $$x^2+kx+1=0$$, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true?

I) k=0

II) k=−1

III) k=−3

A) I only
B) III only
C) I and II only
D) II and III only
E) I and III only

Per the question, $$x^2+kx+1=0$$ with k=constant.

For a quadratic equation ($$ax^2+bx+c=0$$) to have 2 distinct roots ---> $$D =b^2-4ac > 0$$ ---> $$k^2-4>0$$ --->$$k<-2$$or $$k>2$$ . Only III falls in these ranges. B is the correct answer.

how did u get D=b ^ 2-4ac?
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3353
Location: India
GPA: 3.5
In the equation x^2+kx+1=0, x is a variable and k is a constant [#permalink]

### Show Tags

15 Oct 2016, 02:05
1
This post was
BOOKMARKED
jonmarrow wrote:
how did u get D=b ^ 2-4ac?

There are some shortcut formulas -

Quote:
1. b2 −4ac < 0 There are no real roots.
2. b2 −4ac = 0 There is one real root.
3. b2 −4ac > 0 There are two real roots.

We are interested only in the third one here...

So, Engr2012 has used it correctly here..

1. math-algebra-101576.html#p787276
2. http://www.biology.arizona.edu/biomath/ ... roots.html
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2293
Location: United States (CA)
Re: In the equation x^2+kx+1=0, x is a variable and k is a constant [#permalink]

### Show Tags

19 Oct 2017, 10:17
Mascarfi wrote:
In the equation $$x^2+kx+1=0$$, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true?

I) k=0

II) k=−1

III) k=−3

A) I only
B) III only
C) I and II only
D) II and III only
E) I and III only

For a quadratic equation in the form of ax^2 + bx + c = 0, the number of real solutions of the equation is determined by the signed value of the quantity b^2 - 4ac, which is known as the discriminant. The property is:

If b^2 - 4ac > 0, then the quadratic equation ax^2 + bx + c = 0 has two distinct real roots.
If b^2 - 4ac = 0, then the quadratic equation ax^2 + bx + c = 0 has one real root.
If b^2 - 4ac < 0, then the quadratic equation ax^2 + bx + c = 0 has no real roots.

Thus, to make sure x^2 + kx + 1 = 0 has two distinct real roots, we have to make sure k^2 - 4(1)(1) is greater than 0 (notice that a = 1, b = k, and c = 1). That is, we want k^2 - 4 > 0. So let’s check the numbers in the given Roman numerals.

I) k = 0: 0^2 - 4 = -4 > 0? (No)

II) k = -1: (-1)^2 - 4 = -3 > 0? (No)

III) k = -3: (-3)^2 - 4 = 5 > 0? (Yes!)

Thus, only Roman numeral III is correct.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: In the equation x^2+kx+1=0, x is a variable and k is a constant   [#permalink] 19 Oct 2017, 10:17
Display posts from previous: Sort by