Question

the cost of producing x video game consoles, in thousands, is modeled by the following function. if a company spent $1,705 to produce video game consoles, how many consoles were made?
$c(x)=x^4 - 5x^3 - 12x^2 - 22x - 40$
the company made \\(\square\\) video game consoles.

Explanation:

Step1: Set cost equal to 1706

$C(x) = 1706$, so $x^4 - 5x^3 - 12x^2 - 22x - 40 = 1706$

Step2: Rearrange the equation

$x^4 - 5x^3 - 12x^2 - 22x - 1746 = 0$

Step3: Test integer roots (Rational Root Theorem)

Test positive integers: when $x=9$,
$9^4 -5(9)^3 -12(9)^2 -22(9) -1746$
$=6561 - 5(729) -12(81) -198 -1746$
$=6561 - 3645 - 972 - 198 - 1746 = 0$

Step4: Interpret x value

$x$ is in thousands, so total consoles = $9 \times 1000 = 9000$

Answer:

9000