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

Answer:

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

2. $140

Step-by-step 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:

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

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