The volume of a box can be found with the function V, where x is the length of the shortest edge of the box: V(x) = x3 + 5x2 – 14x What is the length of the shortest edge of the box if it has a volume of 30 cubic units? +/-

The length of the shortest edge of the box is 3 units

Step-by-step 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.

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