If x is a positive integer such that x^2 + 5x − 14 = 0, wh

[BTGmoderatorDC]

If x is a positive integer such that x^2 + 5x − 14 = 0, what is the value of x ?

A. −7
B. −5
C. 0
D. 2
E. 5

OA D

Source: Princeton Review

[Brent@GMATPrepNow]

If x is a positive integer such that x² + 5x − 14 = 0, what is the value of x ?

A. −7
B. −5
C. 0
D. 2
E. 5

GIVEN: x² + 5x − 14 = 0
Factor: (x + 7)(x - 2) = 0
So, EITHER x = -7 OR x = 2

Since we're told x is POSITIVE, the correct answer is D

Cheers,
Brent

[swerve]

\begin{align*}
x^2+5x-14 &=0 \\
x^2+7x-2x-14&=0 \\
x(x+7)-2(x+7)&=0\\
(x-2)(x+7)&=0
\end{align*}
Hence
either \(x-2=0 \Rightarrow x=2\)
or \(x+7=0 \Rightarrow x=-7\)

But it is mentioned in the question statement that \(x\) is positive.

Therefore, \(x=2\).

[Scott@TargetTestPrep]

If x is a positive integer such that x^2 + 5x − 14 = 0, what is the value of x ?

A. −7
B. −5
C. 0
D. 2
E. 5

OA D

Source: Princeton Review

x^2 + 5x − 14 = 0

(x + 7)(x - 2) = 0

x = -7 or x = 2

Since x must be positive, 2 is the correct answer.

Alternate solution:

We can eliminate choices A to C since they are not positive. Now, let's check choice D by substituting 2 for the value of x.

2^2 + 5(2) - 14 = 4 + 10 - 14 = 0

We see that choice D is the correct answer.

Answer: D