Answer:
- the only possible value of x is 5
- the dimensions are 2 × 4 × 10
Step-by-step explanation:
The cubic equation ...
(x -3)(x -1)(x +5) = 80
has one real root: x = 5. Using that value for x, the dimensions become ...
length = 5 - 3 = 2
width = 5 - 1 = 4
height = 5 + 5 = 10
The dimensions are (length, width, height) = (2, 4, 10).
_____
We cannot tell the thrust of the problem, since it has only one solution. Perhaps you're supposed to write the cubic in standard form and use the <em>Rational Root theorem</em> to find <em>possible values of x</em>. That form can be found to be ...
(x -3)(x -1)(x +5) -80 = 0
x³ +x² -17x -65 = 0
Descartes' rule of signs tells you there is one positive real root. The rational root theorem tells you possible rational roots are factors of 65:
1, 5, 13, 65
We know that x must be greater than 3 (so all dimensions are positive). Thus <em>possible values of x are 5, 13, 65</em>, and we're pretty sure that 65 is way too large.
