y = 2 ( x - d ) ( x + d ) ( x + g ) ( x

Question

y = 2 ( x - d ) ( x + d ) ( x + g ) ( x - d ) In the given equation, d and g are unique positive constants. When the equation is graphed in the xy -plane, how many distinct x -intercepts does the graph have?

Accepted Answer

Choice B is correct. An x -intercept of a graph in the xy -plane is a point on the graph where the value of y is 0 . Substituting 0 for y in the given equation yields 0 = 2 x - d x + d x + g x - d . By the zero product property, the solutions to this equation are x = d , x = - d , x = - g , and x = d . However, x = d and x = d are identical. It's given that d and g are unique positive constants. It follows that the equation 0 = 2 x - d x + d x + g x - d has 3 unique solutions: x = d , x = - d , and x = - g . Thus, the graph of the given equation has 3 distinct x -intercepts. Choice A is incorrect and may result from conceptual errors. Choice C is incorrect and may result from conceptual errors. Choice D is incorrect and may result from conceptual errors.

Question y-2-x-