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29 Jul 2024, 01:21
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If 2 is one solution of the equation \(x^2 + b^2x = 12\), where \(b\) is a constant, which of the following could be the value of \(bx\)?
I. -12
II. 8
III. 12
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
If 2 is one solution of the equation \(x^2 + b^2x = 12\), where \(b\) is a constant, which of the following could be the value of \(bx\)?
I. -12
II. 8
III. 12
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
29 Jul 2024, 01:21
Kudos
Bookmarks
Official Solution:
If 2 is one solution of the equation \(x^2 + b^2x = 12\), where \(b\) is a constant, which of the following could be the value of \(bx\)?
I. -12
II. 8
III. 12
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
Substituting \(x = 2\) into the equation, we get:
Hence, the equation is \(x^2 + 4x = 12\), which simplifies to \((x - 2)(x + 6) = 0\), and thus \(x = 2\) or \(x = -6\).
Note that the question asks for the value of \(bx\), not \(b^2x\). Since \(b^2 = 4\) gives us \(b = -2\) or \(b = 2\), the possible values for \(bx\) could be \((-2)*2 = -4\), \(2*2 = 4\), \((-2)*(-6) = 12\), and \((-2)*6 = -12\).
Answer: E
If 2 is one solution of the equation \(x^2 + b^2x = 12\), where \(b\) is a constant, which of the following could be the value of \(bx\)?
I. -12
II. 8
III. 12
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
Substituting \(x = 2\) into the equation, we get:
\(4 + 2b^2 = 12\)
\(b^2 = 4\)
\(4 + 2b^2 = 12\)
\(b^2 = 4\)
Hence, the equation is \(x^2 + 4x = 12\), which simplifies to \((x - 2)(x + 6) = 0\), and thus \(x = 2\) or \(x = -6\).
Note that the question asks for the value of \(bx\), not \(b^2x\). Since \(b^2 = 4\) gives us \(b = -2\) or \(b = 2\), the possible values for \(bx\) could be \((-2)*2 = -4\), \(2*2 = 4\), \((-2)*(-6) = 12\), and \((-2)*6 = -12\).
Answer: E
