Answer to Question #269845 in Algebra for pica

Question

Unity Games is a company that sells video games. Its revenue last year was modelled by

the function 𝑔(𝑥) = − 4𝑥^4 + 6𝑥(4𝑥 − 1) − 4 and its revenue this year is modelled by the function 𝑓(𝑥) = − 3𝑥^2(𝑥^2 − 8) − 6𝑥 − 5 where x is the number of video games sold in thousands and revenue is in millions of dollars. Determine the range of values for the number of video games sold that makes the revenue this year greater than the revenue last year. You must use a full algebraic solution.

Answer 1

-4x⁴+6x(4x-1)-4 > -3x²((x²)-8)-6x-5

That is,

-4x⁴+6x(4x-1)-4 - (-3x²(x²-8)-6x-5) > 0

-x²+1 = 0

-(x-1)(x+1)(x²+1) > 0

-1 < x < 1

That is, fewer than 1000 games