GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 12:58

### 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

# One root of the quadratic equation ax^2+bx+c=0

Author Message
TAGS:

### Hide Tags

Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1043
Location: India
GPA: 3.64

### Show Tags

08 Feb 2018, 10:46
1
4
00:00

Difficulty:

65% (hard)

Question Stats:

48% (02:02) correct 52% (02:01) wrong based on 40 sessions

### HideShow timer Statistics

One root of the quadratic equation $$ax^2+bx+c=0$$ is 2 and one root of the quadratic equation $$cx^2+bx+a=0$$ is $$\frac{-1}{3}$$. What is the sum of the roots of the first equation?
A) $$\frac{5}{3}$$
B) -1
C) -2
D) -3
E) -5

_________________
Please give kudos, if you like my post

When the going gets tough, the tough gets going...
Retired Moderator
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82

### Show Tags

08 Feb 2018, 11:14
2
souvonik2k wrote:
One root of the quadratic equation $$ax^2+bx+c=0$$ is 2 and one root of the quadratic equation $$cx^2+bx+a=0$$ is $$\frac{-1}{3}$$. What is the sum of the roots of the first equation?
A) $$\frac{5}{3}$$
B) -1
C) -2
D) -3
E) -5

$$ax^2+bx+c=0$$ Sum of roots of this equation will be $$-\frac{b}{a}$$

as one root is $$2$$ so we have

$$4a+2b+c=0$$------------(1)

$$cx^2+bx+a=0$$ as one root is $$-\frac{1}{3}$$

we have $$\frac{c}{9}-\frac{b}{3}+a=0=>9a-3b+c=0$$-------(2)

subtract equation (1) from (2) we get $$5a-5b=0 => \frac{b}{a}=1$$

so $$-\frac{b}{a}=-1$$

Option B
Manager
Joined: 17 Mar 2015
Posts: 86

### Show Tags

08 Feb 2018, 11:28
souvonik2k wrote:
One root of the quadratic equation $$ax^2+bx+c=0$$ is 2 and one root of the quadratic equation $$cx^2+bx+a=0$$ is $$\frac{-1}{3}$$. What is the sum of the roots of the first equation?
A) $$\frac{5}{3}$$
B) -1
C) -2
D) -3
E) -5

Let m be the second root of first equation and n be the second root of second equation

For First Equation
Sum of roots = -(b/a)
so, m+2 = -(b/a) ------------ (1)

Product of roots = c/a
so, 2m = c/a ---------------(2)

For Second Equation
Sum of roots = -(b/c)
so, m+2 = -(b/c) ------------ (3)

Product of roots = a/c
so, 2m = a/c ---------------(4)

Multiply (2) and (4) and we get m*n = -(3/2)

Multiply (2) and (3) and we get
-(b/a) = (2m)*(n-1/3)

Now -(b/a) = m+2

So, m+2 = (2m)(n-1/3)

we have value of mn so value of m can be obtained from above equation.

m = -3

Sum of roots of first equation = -3+2 = -1

Re: One root of the quadratic equation ax^2+bx+c=0   [#permalink] 08 Feb 2018, 11:28
Display posts from previous: Sort by