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
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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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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