GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 Jan 2020, 06:18

### 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

# If 4 is one solution of the equation x2 + 3x + k = 10, where

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60778
If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

18 Sep 2012, 02:57
4
28
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:44) correct 21% (01:58) wrong based on 1102 sessions

### HideShow timer Statistics

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Practice Questions
Question: 45
Page: 158
Difficulty: 600

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 60778
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

18 Sep 2012, 02:57
16
1
16
SOLUTION

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Viete's formula for the roots $$x_1$$ and $$x_2$$ of equation $$ax^2+bx+c=0$$: $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.

Rewrite the equation given: $$x^2 + 3x +(k-10) =0$$
Thus according to the first property $$4+x_2=-\frac{3}{1}$$ --> $$x_2=-7$$. As we can see we can find the value of $$x_2$$ even without finding the value of $$k$$.

_________________
Manager
Joined: 12 Mar 2012
Posts: 92
Location: India
Concentration: Technology, General Management
GMAT Date: 07-23-2012
WE: Programming (Telecommunications)
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

18 Sep 2012, 06:25
10
2
Bunuel wrote:

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Since 4 is one of the solution, so it must satisfy the equation.
Putting 4 as value of x: 4^2 + 3*4 + k = 10 => k =-18
so the equations is
x^2 + 3x - 28 = 0

Solving this by factorization gives => (x-4)(x+7) = 0
So x = -7 is other solution.

Hence A
_________________
FOCUS..this is all I need!

Ku-Do!
##### General Discussion
Manager
Joined: 25 Jun 2012
Posts: 60
Location: India
WE: General Management (Energy and Utilities)
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

18 Sep 2012, 03:13
4
Slove equation by putting x=4 as it is one of the solution.
u gets value of k=-18

now put k=-18 in the equation,u get eqn in the form of ax^2+bx+c=0. Solving it we get x=4 and x=-7

so other solution is -7.
Senior Manager
Joined: 24 Aug 2009
Posts: 438
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

18 Sep 2012, 05:07
4
Shortcut for the question-

The sum of roots of a equation is = -b/a = -3
One of the given roots is 4
Thus the other root has to be -7
Check = 4-7 = -3 (confirm)

Intern
Joined: 02 Jun 2011
Posts: 48
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

18 Sep 2012, 10:28
2
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Practice Questions
Question: 45
Page: 158
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

One sol. of equation is 4. therefor putting this as X in the equation and finout the constant K.
therefore K = -28.
so, equation can be rewritten as (X-4)(X+7) = 0.

other solution is X = -7.
Intern
Joined: 26 Feb 2015
Posts: 3
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

01 Mar 2015, 19:52
2
You don't need to solve for K, we know that 4 is a solution so we already know one of the terms (x-4)(x+......) we also have x2 + 3x + k = 10, -4 + 7=3 so (x-4)(x+7):0 hence x: -7
Manager
Joined: 10 Apr 2016
Posts: 54
Concentration: Strategy, Entrepreneurship
GMAT 1: 520 Q29 V30
GPA: 3.01
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

18 Apr 2016, 12:48
solving for 4 to find k
16+12+k=10
k=-18
(x^2)+3x-18=10
testing values you find -7
_________________
Took the Gmat and got a 520 after studying for 3 weeks with a fulltime job. Now taking it again, but with 6 weeks of prep time and a part time job. Studying every day is key, try to do at least 5 exercises a day.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2804
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

28 Apr 2016, 07:28
3
Bunuel wrote:
If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Practice Questions
Question: 45
Page: 158
Difficulty: 600

The phrase “4 is one solution of the equation” means that one value of x is 4. Thus, we first must plug 4 for x into the given equation to determine the value of k. So we have

4^2 + (3)(4) + k = 10

16 + 12 + k = 10

28 + k = 10

k = -18

Next we plug -18 into the given equation for k and then solve for x.

x^2 + 3x – 18 = 10

x^2 + 3x – 28 = 0

(x+7)(x-4) = 0

x = -7 or x = 4

Thus, -7 is the other solution. Answer A.
_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 15 Oct 2016
Posts: 12
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

27 Jan 2018, 07:11
put 4 in equation and solve for k
So that gives k = -18
put it back in equation and solve for roots. one will come as 4 and another as -7.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4235
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

27 Jan 2018, 08:09
1
Top Contributor
Bunuel wrote:
If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Let's first determine the value of k.

Since x = 4 is a solution to the equation x² + 3x + k = 10, we know that x = 4 SATISFIES the equation.
That is: 4² + 3(4) + k = 10
Evaluate to get: 16 + 12 + k = 10
Solve for k to get: k = -18

So, the ORIGINAL equation is x² + 3x + (-18) = 10
This is the same as: x² + 3x - 18 = 10
We now need to solve this equation.

First, set it equal to zero: x² + 3x - 28 = 0
Factor: (x + 7)(x - 4) = 0
So, x = -7 or x = 4

We already know that x = 4 is one solution.
So, the other solution is x = -7

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4868
Location: India
GPA: 3.5
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

27 Jan 2018, 08:46
Bunuel wrote:
If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Practice Questions
Question: 45
Page: 158
Difficulty: 600

$$k = 10 - ( x^2 + 3x )$$

Now, $$k = 10 - ( 16 + 12 )$$

Or, $$k = -18$$

Put the value of k as -18 in the equation and solve now

$$x^2 + 3x - 18 = 10$$

$$x^2 + 3x - 28 = 0$$

Actual solving the equation is not required, we already have one value as 4 , so the other value must be -7 ( As -28 = 4*-7), Answer must be (A)
_________________
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 )
VP
Joined: 09 Mar 2016
Posts: 1220
If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

Updated on: 26 Feb 2018, 05:38
Bunuel wrote:
SOLUTION

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Viete's formula for the roots $$x_1$$ and $$x_2$$ of equation $$ax^2+bx+c=0$$: $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.

Rewrite the equation given: $$x^2 + 3x +(k-10) =0$$
Thus according to the first property $$4+x_2=-\frac{3}{1}$$ --> $$x_2=-7$$. As we can see we can find the value of $$x_2$$ even without finding the value of $$k$$.

Hi Bunuel :) , i understand how you soled it, but regardimg Vietas properties $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$

how can i use these properties to find roots for example of this equation $$x^2+16x+64 =0$$

if i follow the first property $$x_1+x_2=-\frac{b}{a}$$ i get $$x_1+x_2 = \frac{64}{1}$$ the same question to the second property ...

on the other hand i know tis rule ---> w

So 64 is our C term
The numbers that can multiply to make 64 are +8 and +8 (8*8 = 64)

16 is our B term

Now find the two factors of C that add up to your B term 8 and 8 Hence 8+8 = 16

Now plug in values I have chosen into factored equation (x+a) (x+b)= 0

(x+8) (x+8)= 0
Now solve for X by equating to 0
(x+8) =0 ---- > x = -8
(x+8)= 0 ----- >x = - 8

But i dont understand how to use these properties to get the same values( -8; -8) $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$

I would appreciate your fantastic explanation

or your mind blowing explanation niks18

Originally posted by dave13 on 21 Feb 2018, 10:15.
Last edited by dave13 on 26 Feb 2018, 05:38, edited 1 time in total.
Intern
Joined: 21 Nov 2017
Posts: 6
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

24 Feb 2018, 07:57
sum of roots is r1+r2= -b/a
here one root is 4
4+r2= -3/1
r2= -3-4 = -7
Retired Moderator
Joined: 25 Feb 2013
Posts: 1153
Location: India
GPA: 3.82
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

26 Feb 2018, 06:21
1
dave13 wrote:
Bunuel wrote:
SOLUTION

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Viete's formula for the roots $$x_1$$ and $$x_2$$ of equation $$ax^2+bx+c=0$$: $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.

Rewrite the equation given: $$x^2 + 3x +(k-10) =0$$
Thus according to the first property $$4+x_2=-\frac{3}{1}$$ --> $$x_2=-7$$. As we can see we can find the value of $$x_2$$ even without finding the value of $$k$$.

Hi Bunuel :) , i understand how you soled it, but regardimg Vietas properties $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$

how can i use these properties to find roots for example of this equation $$x^2+16x+64 =0$$

if i follow the first property $$x_1+x_2=-\frac{b}{a}$$ i get $$x_1+x_2 = \frac{64}{1}$$ the same question to the second property ...

on the other hand i know tis rule ---> w

So 64 is our C term
The numbers that can multiply to make 64 are +8 and +8 (8*8 = 64)

16 is our B term

Now find the two factors of C that add up to your B term 8 and 8 Hence 8+8 = 16

Now plug in values I have chosen into factored equation (x+a) (x+b)= 0

(x+8) (x+8)= 0
Now solve for X by equating to 0
(x+8) =0 ---- > x = -8
(x+8)= 0 ----- >x = - 8

But i dont understand how to use these properties to get the same values( -8; -8) $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$

I would appreciate your fantastic explanation

or your mind blowing explanation niks18

Hi dave13,

Here is the generic quadratic equation $$ax^2+bx+c$$ and here is your equation $$x^2+16x+64 =0$$. Now match both the coefficients of both the equations and tell me what will be the value of a, b & c as per your equation?

if you get the values of a, b & c

then calculate sum of roots $$= -\frac{b}{a}$$

and product of roots $$= \frac{c}{a}$$
VP
Joined: 09 Mar 2016
Posts: 1220
If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

26 Feb 2018, 06:46
niks18 wrote:
dave13 wrote:
Bunuel wrote:
SOLUTION

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Viete's formula for the roots $$x_1$$ and $$x_2$$ of equation $$ax^2+bx+c=0$$: $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.

Rewrite the equation given: $$x^2 + 3x +(k-10) =0$$
Thus according to the first property $$4+x_2=-\frac{3}{1}$$ --> $$x_2=-7$$. As we can see we can find the value of $$x_2$$ even without finding the value of $$k$$.

Hi Bunuel , i understand how you soled it, but regardimg Vieta`s properties $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$

how can i use these properties to find roots for example of this equation $$x^2+16x+64 =0$$

if i follow the first property $$x_1+x_2=-\frac{b}{a}$$ i get $$x_1+x_2 = \frac{64}{1}$$ the same question to the second property ...

on the other hand i know tis rule ---> w

So 64 is our C term
The numbers that can multiply to make 64 are +8 and +8 (8*8 = 64)

16 is our B term

Now find the two factors of C that add up to your B term 8 and 8 Hence 8+8 = 16

Now plug in values I have chosen into factored equation (x+a) (x+b)= 0

(x+8) (x+8)= 0
Now solve for X by equating to 0
(x+8) =0 ---- > x = -8
(x+8)= 0 ----- >x = - 8

But i dont understand how to use these properties to get the same values( -8; -8) $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$

I would appreciate your fantastic explanation

or your mind blowing explanation niks18

Hi dave13,

Here is the generic quadratic equation $$ax^2+bx+c$$ and here is your equation $$x^2+16x+64 =0$$. Now match both the coefficients of both the equations and tell me what will be the value of a, b & c as per your equation?

if you get the values of a, b & c

then calculate sum of roots $$= -\frac{b}{a}$$

and product of roots $$= \frac{c}{a}$$

Hi niks18, glad to hear from you

$$x^2+16x+64 =0$$ from this I can clearly see that

$$x^2$$ is $$a$$ it can be considered as 1 since no number is given

16 is $$b$$

64 is $$c$$

so you say --->

then calculate sum of roots $$= -\frac{b}{a}$$ ok that means $$-\frac{16}{1}$$

and product of roots $$= \frac{c}{a}$$ and this means $$\frac{64}{1}$$

so what next
Retired Moderator
Joined: 25 Feb 2013
Posts: 1153
Location: India
GPA: 3.82
If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

26 Feb 2018, 08:29
1
Quote:
Hi niks18, glad to hear from you

$$x^2+16x+64 =0$$ from this I can clearly see that

$$x^2$$ is $$a$$ it can be considered as 1 since no number is given

16 is $$b$$

64 is $$c$$

so you say --->

then calculate sum of roots $$= -\frac{b}{a}$$ ok that means $$-\frac{16}{1}$$

and product of roots $$= \frac{c}{a}$$ and this means $$\frac{64}{1}$$

so what next

Hi dave13,

what is your objective here? Do you want to find out the roots of the equation?. If yes then that could be done by two ways - one by factorization and second by using the discriminant formula.

what you did above was you found out the relationship between the roots i.e their sum and product. Now if you are given one root, then using this relationship you can find out the other.

So kindly clarify what is your objective
SVP
Joined: 03 Jun 2019
Posts: 1950
Location: India
GMAT 1: 690 Q50 V34
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where  [#permalink]

### Show Tags

15 Sep 2019, 05:12
Bunuel wrote:
If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Practice Questions
Question: 45
Page: 158
Difficulty: 600

Let the other solution be x
x+4 = -3
x= -7

IMO A

Posted from my mobile device
Re: If 4 is one solution of the equation x2 + 3x + k = 10, where   [#permalink] 15 Sep 2019, 05:12
Display posts from previous: Sort by