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# If -4 is one solution to the equation x^2+bx+c=0,where b and c

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Senior Manager
Joined: 26 Dec 2015
Posts: 277
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
If -4 is one solution to the equation x^2+bx+c=0,where b and c [#permalink]

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Updated on: 23 Apr 2017, 08:08
1
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:52) correct 31% (01:51) wrong based on 49 sessions

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If -4 is one solution to the equation $$x^{2}$$+bx+c=0, where b and c are constants, and b+c=-21, what is the other solution?

A) -5

B) -1

C) 5

D) 7

E) 10

Originally posted by LakerFan24 on 23 Apr 2017, 07:46.
Last edited by stonecold on 23 Apr 2017, 08:08, edited 1 time in total.
Edited the topic.
Manager
Joined: 25 Apr 2016
Posts: 57
Re: If -4 is one solution to the equation x^2+bx+c=0,where b and c [#permalink]

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23 Apr 2017, 07:59
x^2 + bx + c =0 and -4 is one of the solution => 16+(-4)b+c=0=> 4b-c=16 and given b+c =-21; solving simultaneous equations would give b=-1
now, sum of the roots = -b/1 =>-4 + other root = 1 => other solution = 5 => option C
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Re: If -4 is one solution to the equation x^2+bx+c=0,where b and c [#permalink]

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23 Apr 2017, 08:04
1
Hi LakerFan24
There are a number of methods to solve this one.
But let me iterate a method that will be helpful in solving some difficult questions as well.

Quote:
For any algebraic expression of the form ax^2 + bx +c => Sum of roots = -b/a and product of roots =c/a

So for the equation x^2+bc+c => Product of roots => c/1 =c

One of the roots =-4
Hence putting x=-4 in the equation => 4b-c=16
Also we are told that b+c=21
Hence b=-1 and c=-20

Thus product of roots =-20
One of them is -4
Let the other one be G
G*(-4)=-20

G=5

Now, there are other methods which are 10000X times simpler then this one.
But as i said => This concept of sum and product of roots is helpful in some difficult questions as well.

Regards
Stone Cold

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If -4 is one solution to the equation x^2+bx+c=0,where b and c [#permalink]

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23 Apr 2017, 13:29
LakerFan24 wrote:
If -4 is one solution to the equation $$x^{2}$$+bx+c=0, where b and c are constants, and b+c=-21, what is the other solution?

A) -5

B) -1

C) 5

D) 7

E) 10

b=-21-c
(-4)^2+(-21-c)(-4)+c=0
c=-20
b=-1
x^2-x-20=0
(x+4)(x-5)=0
other solution: x=5
C
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Joined: 02 Sep 2009
Posts: 46047
Re: If -4 is one solution to the equation x^2+bx+c=0,where b and c [#permalink]

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23 Apr 2017, 22:21
LakerFan24 wrote:
If -4 is one solution to the equation $$x^{2}$$+bx+c=0, where b and c are constants, and b+c=-21, what is the other solution?

A) -5

B) -1

C) 5

D) 7

E) 10

Similar question from Official Guide: https://gmatclub.com/forum/if-4-is-one- ... 39119.html

Hope it helps.
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Re: If -4 is one solution to the equation x^2+bx+c=0,where b and c   [#permalink] 23 Apr 2017, 22:21
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