Question

Consider the equation |(x-3)^2-4|=b. Determine the value of b so that the equation has no solution.

Answer 1

As an absolute value makes any value positive, any negative value of b will cause the equation to be unsolvable. 

Answer 2

|(x-3)^2-4|=b  since this is an absolute value equation

b can have any value less than zero so that the above is never true, in interval notation:

b=(-oo,0)