Answer:
The length of the shortest edge of the box is 3 units
Explanation:
Since the volume of the box is given by the function
V(x) = x³ + 5x² – 14x
Where V is the volume and x if the length of the shortest edge of the box.
To determine the length of the shortest edge of the box if it has a volume of 30 cubic units, we will put V(x) = 30 and then find the value of x.
30 = x³ + 5x² – 14x
∴ x³ + 5x² – 14x – 30 = 0
The solution to the cubic equation is shown in the attachments below.
x₁ = 3 , x₂ = – 1.55, and x₃ = – 6.45
Since the length cannot be negative, the length of the shortest edge of the box is 3 units.