The area of a rectangle can be represented by:

(ii) Given that this quadratic expression represents the area of a rectangle, what would be
the possible values of ?
Justify your answer:

To find the possible values of that make the area of the rectangle valid, we need to determine the roots of the quadratic expression using the quadratic formula:

Here, , , and . Plugging in these values gives:

Calculating the two potential solutions, we have and . Since represents a physical length, it must be non-negative, thus the only possible value for is units.

As for the broader implications, the quadratic function represents a physical space; thus, practical applications like architectural design or landscaping would require dimensions to always be positive. It’s a fun challenge to ensure the math translates into real-world scenarios!