A rectangular park is to be designed so that its perimeter is 20 m and its area is 30 m2.
(i) Let the breadth of the park be x metres and express the length in terms of x.
(ii) Form a quadratic equation in x that must be satisfied if such a park is to exist.
(iii) Find the discriminant of the equation obtained in part (ii) and hence determine the nature of its roots.
(iv) Using your result from part (iii), explain whether a rectangle having both the stated perimeter and area can actually be constructed.