10
advanced-math

Revenue is given by R(x)=(100−x)(20+x)R(x) = (100 - x)(20 + x). Find the x-intercepts of this function.

A

x=100,−20x = 100, -20

B

x=−100,20x = -100, 20

C

x=100,20x = 100, 20

D

x=−100,−20x = -100, -20

Correct Answer: A

Choice A is the correct answer. The x-intercepts occur where R(x)=0R(x) = 0.

  1. Set the equation to zero: (100−x)(20+x)=0(100 - x)(20 + x) = 0.
  2. Apply Zero Product Property:
    • 100−x=0⇒x=100100 - x = 0 \Rightarrow x = 100
    • 20+x=0⇒x=−2020 + x = 0 \Rightarrow x = -20

These points represent the prices or quantities where revenue is zero.

Choice B is incorrect because of sign errors. Choice C is incorrect because 20+x=020+x=0 gives −20-20. Choice D is incorrect because 100−x=0100-x=0 gives 100100.

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