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In the equation x^2 + 5x + k = 0

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In the equation x^2 + 5x + k = 0

by swerve » Mon Oct 30, 2017 8:51 am
In the equation
$$x^2+5x+k=0$$
k is a constant and x is a variable. What is the value of k?

$$(A)\ 2\ is\ a\ root\ of\ x^2+5x+k=0.$$
$$(B)\ (x+7)\ is\ a\ factor\ of\ x^2+5x+k=0.$$

The OA is D.

I need help to solve this DS question. Please, can any expert explain it for me? Thanks.
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Source: — Data Sufficiency |

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by ErikaPrepScholar » Tue Oct 31, 2017 10:07 am
This question requires us to understand that if a is a root of an equation, then (x-a) is a factor of the same equation.

Statement 1

If 2 is a root of the equation, then (x-2) is a factor. This means that the other factor must be (x+7), so that when we FOIL (x-2)(x+7), we end up with 5x as the middle term (7x - 2x = 5x). This gives us x^2 + 5x - 14, so k = 14. Sufficient.

Statement 2

If (x+7) is a factor, the other factor must be (x-2), as explained above. This gives x^2 + 5x - 14 as our equation, so k - 14. Sufficient.
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