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In the equation (αx + 3)2 = 36, a is a constant. If x = − 3 is one solution to the equation, what is a possible value of α?
- a)−11
- b)−5
- c)−1
- d)0
Correct answer is option 'C'. Can you explain this answer?
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In the equation (αx + 3)2 = 36, a is a constant. If x = − ...
Choice C is correct. Since x = −3 is a solution to the equation, substituting −3 for x gives (−3α + 3)2 = 36. Taking the square root of each side of this equation gives the two equations −3α + 3 = 6 and −3α + 3 = −6. Solving each of these for a yields α = −1 and α = 3. Therefore, −1 is a possible value of α.
Choice A is incorrect and may be the result of ignoring the squared expression and solving −3α + 3 = 36 for α. Choice B is incorrect and may be the result of dividing 36 by 2 instead of taking the square root of 36 when solving for a. Choice D is incorrect and may be the result of taking the sum of the value of x, −3, and the constant, 3.
Choice A is incorrect and may be the result of ignoring the squared expression and solving −3α + 3 = 36 for α. Choice B is incorrect and may be the result of dividing 36 by 2 instead of taking the square root of 36 when solving for a. Choice D is incorrect and may be the result of taking the sum of the value of x, −3, and the constant, 3.
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In the equation (αx + 3)2 = 36, a is a constant. If x = − 3 is one solution to the equation, what is a possible value of α?a)−11b)−5c)−1d)0Correct answer is option 'C'. Can you explain this answer?
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