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Which of the following is a solution to the equation x^2+40x+336=0?

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Which of the following is a solution to the equation x^2+40x+336=0? [#permalink]

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80% (01:36) correct 20% (01:52) wrong based on 140 sessions

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Re: Which of the following is a solution to the equation x^2+40x+336=0? [#permalink]

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New post 22 Feb 2017, 02:42
Bunuel wrote:
Which of the following is a solution to the equation x^2+40x+336=0?

A. -6
B. -12
C. 12
D. 26
E. 58


\(x^2+40x+336=0\)
(x+12)(x+28)=0
x=-12 or x=-28

OR

substitute each of the options in place of x and check if \(x^2+40x+336=0\)
Only -12 satisfies the equation

Hence Option B is correct
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Re: Which of the following is a solution to the equation x^2+40x+336=0? [#permalink]

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Bunuel wrote:
Which of the following is a solution to the equation x² + 40x + 336 = 0?

A. -6
B. -12
C. 12
D. 26
E. 58


As with most quadratic equations, we can solve this equation by factoring the left side x² + 40x + 336
To factor this, we must find two values that have a sum 40 and a product of 336.
This might prove a little tricky for many.
0akshay0 showed that we can factor this left side to get (x+12)(x+28)=0


I want to show that the alternative approach of testing values isn't as time-consuming as we might first think.
In fact, if we recognize that the correct answer must be NEGATIVE, then we can solve this quickly.

How do I know that x must be NEGATIVE?
Well, if x is POSITIVE, then each term in the expression x² + 40x + 336 will evaluate to be POSITIVE
That is, if x is POSITIVE, then x² is POSITIVE, and 40x is POSITIVE
So, if x is POSITIVE then x² + 40x + 336 = POSITIVE + POSITIVE + 336
As you can see, if x is POSITIVE, then it's impossible for x² + 40x + 336 to equal 0
So, we can ELIMINATE answer choices C, D and E

At this point, we only need to test ONE of the two remaining answer choices.
If we test A and it works, then we're done. The correct answer is A.
If we test A and it doesn't work, then we're done. The correct answer is B.

So, let's test A (x = -6).
Replace x with -6 to get: (-6)² + 40(-6) + 336 = 0
Simplify: 36 - 240 + 336 = 0
Evaluate: 132 = 0
DOESN'T WORK
So, ELIMINATE A

Answer: B

Cheers,
Brent
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Re: Which of the following is a solution to the equation x^2+40x+336=0? [#permalink]

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New post 22 Feb 2017, 09:55
Bunuel wrote:
Which of the following is a solution to the equation \(x^2+40x+336=0\)?

A. -6
B. -12
C. 12
D. 26
E. 58


\(x^2+40x+336=0\)

Or, \(x^2+12x + 28x +336=0\)

Or, \(x (x +12 ) + 28 ( x +12 )=0\)

Or, \((x +12 )( x + 28 )=0\)

So, x = - 12 , - 28

Thus, answer must be (B) -12
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Re: Which of the following is a solution to the equation x^2+40x+336=0? [#permalink]

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New post 22 Feb 2017, 10:39
x1+x2 = -40
x1*x2 = 336.

Definitely roots are negative. - 6*-34 is no where close to 336. So answer is -12. B
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Re: Which of the following is a solution to the equation x^2+40x+336=0? [#permalink]

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New post 21 May 2017, 11:22
GMATPrepNow wrote:
Bunuel wrote:
Which of the following is a solution to the equation x² + 40x + 336 = 0?

A. -6
B. -12
C. 12
D. 26
E. 58


As with most quadratic equations, we can solve this equation by factoring the left side x² + 40x + 336
To factor this, we must find two values that have a sum 40 and a product of 336.
This might prove a little tricky for many.
0akshay0 showed that we can factor this left side to get (x+12)(x+28)=0


I want to show that the alternative approach of testing values isn't as time-consuming as we might first think.
In fact, if we recognize that the correct answer must be NEGATIVE, then we can solve this quickly.

How do I know that x must be NEGATIVE?
Well, if x is POSITIVE, then each term in the expression x² + 40x + 336 will evaluate to be POSITIVE
That is, if x is POSITIVE, then x² is POSITIVE, and 40x is POSITIVE
So, if x is POSITIVE then x² + 40x + 336 = POSITIVE + POSITIVE + 336
As you can see, if x is POSITIVE, then it's impossible for x² + 40x + 336 to equal 0
So, we can ELIMINATE answer choices C, D and E

At this point, we only need to test ONE of the two remaining answer choices.
If we test A and it works, then we're done. The correct answer is A.
If we test A and it doesn't work, then we're done. The correct answer is B.

So, let's test A (x = -6).
Replace x with -6 to get: (-6)² + 40(-6) + 336 = 0
Simplify: 36 - 240 + 336 = 0
Evaluate: 132 = 0
DOESN'T WORK
So, ELIMINATE A

Answer: B

Cheers,
Brent



This is a great approach Brent! When I solved this I took almost 3.5 mins - But your approach is best.
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Re: Which of the following is a solution to the equation x^2+40x+336=0?   [#permalink] 21 May 2017, 11:22
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