Answer:
9 game consoles
Step-by-step explanation:
I find it convenient to use a graphing calculator or spreadsheet program to solve higher-degree polynomial equations. The attached shows the solution to be x = 9.
9 consoles were made.
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Descartes' rule of signs tells you there is one positive real root to the equation ...
x^4 -5x^3 -12x^2 -22x -1746 = 0
The factors of 1746 are 1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746. If the solution is rational, it is one of these numbers. Since the equation can be rearranged to ...
x^4 = 1746 +22x +12x^2 +5x^3
we know the value of x will be more than the fourth root of 1746 ≈ 6.46. That suggests 9 as a reasonable first guess. Evaluating c(x) for x=9 gives 1706, the value we're looking for.
