x 2 - 2 x - 9 = 0 One solution to the given equation can be written as 1

Question

x 2 - 2 x - 9 = 0 One solution to the given equation can be written as 1 + k , where k is a constant. What is the value of k ?

Accepted Answer

Choice B is correct. Adding 9 to each side of the given equation yields x 2 - 2 x = 9 . To complete the square, adding 1 to each side of this equation yields x 2 - 2 x + 1 = 9 + 1 , or x - 1 2 = 10 . Taking the square root of each side of this equation yields x - 1 = /mo> 10 . Adding 1 to each side of this equation yields x = 1 /mo> 10 . Since it's given that one of the solutions to the equation can be written as 1 + k , the value of k must be 10 . Alternate approach: It's given that 1 + k is a solution to the given equation. It follows that x = 1 + k . Substituting 1 + k for x in the given equation yields 1 + k 2 - 2 1 + k - 9 = 0 , or 1 + k 1 + k - 2 1 + k - 9 = 0 . Expanding the products on the left-hand side of this equation yields 1 + 2 k + k - 2 - 2 k - 9 = 0 , or k - 10 = 0 . Adding 10 to each side of this equation yields k = 10 . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question x-2-2-