A gardener wants to build a rectangular flower bed of area 120 m2. He decides that the length of the bed should exceed its breadth by p metres, where p is a positive real number chosen later.
a. (i) Let the breadth be x metres. Form a quadratic equation in x in terms of p that represents the given conditions.
b. (ii) Using your equation, obtain the condition on p that ensures the dimensions of the bed are real (i.e. he breadth is a real number).
c. (iii) Applying the additional requirement that the length and breadth must be distinct, find the range of positive values of p that satisfy this condition.