Question

A box has a volume of 1008 cubic inches. Your friend told you that he found thepolynomial that represents the volume of the box: 4x3-28x2 +144x. If x is the height ofthe box, how tall is the box?

Answer 1

Given:

The expression for the volume of box in terms of x is,

$4x^3-28x^2+144x$

Explanation:

The volume of cube is 1008. So equation for x is,

$\begin{gathered} 4x^3-28x^2+144x=1008 \\ 4x^3-28x^2+144x-1008=0 \end{gathered}$

To determine the value of x, plot the equation on the graph.

Since the root of the equation is 7 and two remaining roots are imaginary. So possible value of x is 7, as height can never be imaginary value.

So box is 7 inches tall.

Answer: 7 inches