the revenue of this product is given by R=px=(100x-x^2)x. how many units must be sold to give zero revenue? p=100x-x^2

R(x) is the revenue as a function of the number of units sold, x, where

R(x)=(100x-x²)x

if p(x)=100x-x² then R(x)=0 whenever p=0.

So the problem would be reduced to solve for p(x)=0, or
100x-x²=0
x(100-x)=0
which gives us x=100 would make p(x)=0 and R(x)=0.

Put x=100 back into R(x) to make sure the answer is correct.

To find the number of units that must be sold to give zero revenue, we need to set the revenue equation equal to zero.

The revenue equation is given by R = px = (100x - x^2)x.

Setting this equal to zero, we have:

0 = (100x - x^2)x

To solve this equation, we can factor out an "x" from the equation:

0 = x(100 - x)x

This equation can be true if one of the terms on the right-hand side is equal to zero. So, we have two possibilities:

1) x = 0
2) 100 - x = 0

Solving the first possibility, x = 0 implies that no units are sold. This means that the revenue will be zero.

Solving the second possibility, 100 - x = 0, we find x = 100. This means that 100 units must be sold to give zero revenue.

Therefore, either no units (x = 0) or 100 units (x = 100) must be sold to give zero revenue.