15 The revenue from the sale of a product is given by R1537x

15) The revenue from the sale of a product is given by R=1537x-84x^2-x^3. if the sale of 7 units gives the total revenue of $6300, use synethic devision to find another number of units that will give $6300 in revenue.

What is another number of units that will give $6300 in revenue? ________ units

(share all work for PRECALC problem)

Solution

R=1537x-84x²-x³,sale of 7 units gives the total revenue of $6300

6300=1537x-84x²-x³

x³+84x²-1537x+6300=0 , x=7 is root of the equation

synthetic division:

7)...1....84....-1537.....6300
..............7.......637.....6300
------------------------------------------------
......1....91....-900...........0

quadratic factor is x²+91x-900

for other solution

x²+91x-900=0

x²+100x-9x-900=0

x(x+100)-9(x+100)=0

(x+100)(x-9)=0

x=-100,x=9

x cannot be negative

so,another number of units that will give $6300 in revenue is ____9____ units