Question

1) Which of the equivalent expressions for P(x) reveals the price which gives a profit of

zero without changing the form of the expression?
P(x) = -3x? + 432x - 1680
b) P(x) = -3(x-4)(x - 140)
P(x) = -3(x - 72)2 + 13872
2) Find a price, which gives a profit of zero.

Answer 1

1. (B)P(x) = -3(x-4)(x - 140)

2. $140

Explanation:

(1) Given the profit function, P(x) where x is the price, the expression which reveals the price which gives a profit of zero without changing the form of the expression is:

P(x) = -3(x-4)(x - 140)

This is as a result of the fact that equating it to zero immediately yields the zeros of the quadratic polynomial.

(2)When the profit, P(x)=0, then using the expression above we have:

`P(x) = -3(x-4)(x - 140)\\Since -3\\eq 0, then:\\x-4=0$ or x-140=0\\x=4 or x=140`

A price of $4 or $140 as the case may be gives a profit of zero.