Read the following situation and answer the questions that follow.
A rectangular garden has numerical length ℓ metres and breadth b metres. The perimeter of the garden is 26 metres and its area is 40 square metres.
a. (i) Express ℓ and b in terms of their sum and product, and write down these two numerical values.
b. (ii) Taking ℓ and b as the zeros, construct the monic quadratic polynomial whose zeros represent the two dimensions of the garden.
c. (iii) Factorise the polynomial of part (ii) to determine the exact numerical values of ℓ and b.
d. (iv) Show that the dimensions you have obtained satisfy both the given perimeter and area conditions.