Question

Carmen is using the quadratic equation (x + 15)(x) = 100 where x represents the width of a picture frame. Which statement about the solutions x = 5 and x = –20 is true?
The solutions x = 5 and x = –20 are reasonable.
The solution x = 5 should be kept, but x = –20 is unreasonable.
The solution x = –20 should be kept, but x = 5 is unreasonable.
The solutions x = 5 and x = –20 are unreasonable.

Answer 1

The solution x = 5 should be kept, but x = –20 is unreasonable.

Reason: x is a width (must be positive). x = 5 gives positive dimensions (x = 5, x + 15 = 20), while x = –20 is a negative width and not physically meaningful.