In the equation \(x^2 + bx + 12 = 0,\) \(x\) is a variable and \(b\) is a constant. What is the value of \(b?\)

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In the equation \(x^2 + bx + 12 = 0,\) \(x\) is a variable and \(b\) is a constant. What is the value of \(b?\)

(1) \(x - 3\) is a factor of \(x^2 + bx + 12.\)
(2) \(4\) is a root of the equation \(x^2 + bx + 12 = 0.\)

Answer: D

Source: Official Guide

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Vincen wrote:
Wed Oct 28, 2020 8:42 am
In the equation \(x^2 + bx + 12 = 0,\) \(x\) is a variable and \(b\) is a constant. What is the value of \(b?\)

(1) \(x - 3\) is a factor of \(x^2 + bx + 12.\)
(2) \(4\) is a root of the equation \(x^2 + bx + 12 = 0.\)

Answer: D

Source: Official Guide
Solution:

We need to determine the value of b where b is a constant in the equation x^2 + bx + 12 = 0,

Statement One Alone:

Since x - 3 is a factor of x^2 + bx + 12, x = 3 is a solution of the equation x^2 + bx + 12 = 0. Therefore, we have:

3^2 + b(3) + 12 = 0

9 + 3b + 12 = 0

3b = -21

b = -7

Statement one alone is sufficient.

Statement Two Alone:

Since 4 is a root of the equation x^2 + bx + 12 = 0, we have:

4^2 + b(4) + 12 = 0

16 + 4b + 12 = 0

4b = -28

b = -7

Statement two alone is sufficient.

Answer: D

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